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## Signatures of short distance physics in the cosmic microwave background,” Phys

Venue: | Rev. D |

Citations: | 46 - 2 self |

### Citations

811 | Particle physics and Inflationary cosmology
- Linde
- 1980
(Show Context)
Citation Context ...e CMBR, whose power is proportional to (H/m4) 2 , where m4 is the (reduced) four dimensional Planck length. So measurements of this power give a direct measurement of 1 For textbook introductions see =-=[1]-=-[2][3]. 1H. COBE [6] data already provide the interesting upper bound H < 10 14 GeV which corresponds to vacuum energies ∼ 10 16 GeV, the supersymmetric unification scale. Intensive efforts are under... |

704 |
The Early Universe (Addison-Wesley
- Kolb, Turner
- 1990
(Show Context)
Citation Context ...MBR, whose power is proportional to (H/m4) 2 , where m4 is the (reduced) four dimensional Planck length. So measurements of this power give a direct measurement of 1 For textbook introductions see [1]=-=[2]-=-[3]. 1H. COBE [6] data already provide the interesting upper bound H < 10 14 GeV which corresponds to vacuum energies ∼ 10 16 GeV, the supersymmetric unification scale. Intensive efforts are under wa... |

660 | The Hierarchy Problem and New Dimensions at a Millimeter”, Phys
- Arkani-Hamed, Dimopoulos, et al.
- 1998
(Show Context)
Citation Context ...by powers of 1/H will lead to phenomenologically acceptable lifetimes. One could achieve this, for example, if some discrete subgroup of the U(1) baryon number symmetry was gauged, along the lines of =-=[36,37]-=-. Since we are not studying our models in detail we will leave this issue aside. 4.4. The Hoˇrava-Witten model Compactifications of M-theory on X11 = X10 × S 1 /Z2 were the first known M-theory models... |

325 |
New dimensions at a millimeter to a Fermi and superstrings at a TeV,” Phys
- Antoniadis, Arkani-Hamed, et al.
- 1998
(Show Context)
Citation Context ...by powers of 1/H will lead to phenomenologically acceptable lifetimes. One could achieve this, for example, if some discrete subgroup of the U(1) baryon number symmetry was gauged, along the lines of =-=[36,37]-=-. Since we are not studying our models in detail we will leave this issue aside. 4.4. The Hoˇrava-Witten model Compactifications of M-theory on X11 = X10 × S 1 /Z2 were the first known M-theory models... |

304 |
Cosmological Inflation and Large-Scale Structure
- Liddle, Lyth
- 2000
(Show Context)
Citation Context ..., whose power is proportional to (H/m4) 2 , where m4 is the (reduced) four dimensional Planck length. So measurements of this power give a direct measurement of 1 For textbook introductions see [1][2]=-=[3]-=-. 1H. COBE [6] data already provide the interesting upper bound H < 10 14 GeV which corresponds to vacuum energies ∼ 10 16 GeV, the supersymmetric unification scale. Intensive efforts are under way t... |

239 |
Superstring Theory Vol
- Green, Schwartz, et al.
- 1987
(Show Context)
Citation Context ...cales, including the fundamental scale, are close to MGUT and supergravity is valid. The GUT group is broken to the standard model gauge group by visible sector gauge field configurations on X – c.f. =-=[40]-=- for a discussion. Therefore we let LCY = V 1/6 X Newton’s constant GN and the GUT coupling αGUT can be written as [13]: −1 = MGUT . 1 8πGN = VXL11 κ 2 11 αGUT = g2 GUT 4π = ( ) 2 2/3 4πκ11 2VX (4.28)... |

235 |
Strong coupling expansion of Calabi-Yau compactification. Nucl. Phys
- Witten
- 1996
(Show Context)
Citation Context ...lly viable string and M-theory models, the fundamental scale Mf – either the higherdimensional Planck scale or the string scale – is lower than the 4D Planck scale m4 by up to two orders of magnitude =-=[31,32,13]-=-. If we compactify a d-dimensional theory with Planck scale Mf on a (d−4)-dimensional manifold Xd−4 with volume Vd−4, then m 2 4 = Md−2 f Vd−4. The high scale m4 is not a dynamical scale, but rather a... |

160 |
Supersymmetric Standard Models, Flux Compactification and Moduli Stabilization,” arXiv:hep-th/0409032
- Cvetic, Liu
(Show Context)
Citation Context ...1 vacua. Few compact examples are known but one may appeal to heterotic-M theory duality in seven dimensions to make some arguments about their structure [14,15]. For another related construction see =-=[43]-=-. Calabi-Yau threefolds with geometric mirror partners are believed to be T 3 fibrations over an S 3 base [44]. Now heterotic string theory on T 3 is dual to M theory on K3, so if the base is large an... |

136 | Cosmological breaking of supersymmetry or little Lambda goes back to the future
- Banks
(Show Context)
Citation Context ...2 /M 2 ) + c1p 2 (H 2 /M 2 ) + c2p 4 /M 2 + c3p 4 /M 2 (H 2 /M 2 ) + c4p 6 /M 4 + . . .}. (3.1) 2 For an example of a speculation on how locality might break down in de Sitter space string theory see =-=[30]-=-. 18This structure follows from the fact that only even powers of momenta are allowed, and that the curvature is ∼ H2 . Therefore, no odd powers of M can appear. Information about new physics is cont... |

118 |
Mirror symmetry is T-duality, Nucl. Phys. B479
- Strominger, Yau, et al.
- 1996
(Show Context)
Citation Context ...o make some arguments about their structure [14,15]. For another related construction see [43]. Calabi-Yau threefolds with geometric mirror partners are believed to be T 3 fibrations over an S 3 base =-=[44]-=-. Now heterotic string theory on T 3 is dual to M theory on K3, so if the base is large and we stay away from the singular fibers, we can claim that the heterotic string on a Calabi-Yau threefold is d... |

110 |
Evidence for Heterotic
- Polchinski, Witten
- 1996
(Show Context)
Citation Context ...not clear that the expressions for the gauge couplings are correct. Instead we can appeal to string duality [13]. The strong coupling limit of the SO(32) string is weakly coupled type I string theory =-=[35]-=-. The strong coupling limit of the E8 ×E8 heterotic string compactified on X is M-theory on X×S 1 /Z2 [33]. In this latter limit, gauge coupling unification is compatible with a background well descri... |

96 | Holography and cosmology
- Fischler, Susskind
- 1998
(Show Context)
Citation Context ...refore obey cosmic no-hair theorem, and in ation will succeed in getting rid of initial inhomogeneities. This may be viewed as another example of the cosmological variant of the holographic principle =-=[19]-=-[20]. The structure of the spacetime is fully coded on the preferred screen, i.e. the apparent horizon. Its area is small during in ation because H must be large, and hence the Hubble region is censor... |

88 |
Natural inflation with pseudo - Nambu-Goldstone bosons
- Freese, Frieman, et al.
- 1990
(Show Context)
Citation Context ... is then formally defined as the regime |η|, |ǫ| ≪ 1. The relative importance of these parameters depends on the model of inflation. For example, as we will see below in the case of natural inflation =-=[17]-=-, or modular inflation, [18], ǫ ≪ η. Thus the deviations from slow roll are mainly coded in the parameter η. In contrast, in the simplest model of chaotic inflation driven by a mass term, ǫ ∼ m2 /H2 >... |

72 |
Trans-Planckian problem of inflationary cosmology”, Phys
- Martin, Brandenberger
- 2001
(Show Context)
Citation Context ...lation. There have been a number of investigations of the signature of high energy scale physics in the CMBR. Heavy particles produced by parametric resonance have been studied in [7]. Several groups =-=[8,9,10,11,12]-=- have studied the effect that simple phenomenological models of stringy corrections to gravity would have on the inflationary fluctuation spectrum in the CMBR. This work shares many features with the ... |

62 |
Evidence for Heterotic - Type I String Duality,” Nucl. Phys
- Polchinski, Witten
- 1996
(Show Context)
Citation Context ...not clear that the expressions for the gauge couplings are correct. Instead we can appeal to string duality [13]. The strong coupling limit of the SO(32) string is weakly coupled type I string theory =-=[35]-=-. The strong coupling limit of the E8E8 heterotic string compactied onX is M-theory on XS1=Z2 [33]. In this latter limit, gauge coupling unication is compatible with a background well described by... |

53 |
String theory and quintessence
- Hellerman, Kaloper, et al.
(Show Context)
Citation Context ...t of information can fit in the interior. Moreover, most of the objects inside the Hubble region are in the thermal bath of fluctuations located in the region when the apparent horizon is almost null =-=[21]-=-, with the cosmological Hawking temperature TH = H/2π. Since the inflaton is much lighter than the Hubble scale during inflation, the interactions with the thermal quanta cause its vev and the backgro... |

46 |
Spontaneous creation of almost scale-free density perturbations in an inflationary Universe, Phys
- Bardeen, Steinhardt, et al.
- 1983
(Show Context)
Citation Context ...ing inflation, and which is approximately constant between this time, and when the mode re-enters the cosmological horizon later. At this later time ζ is well approximated by δρ/ρ, establishing (2.8) =-=[24]-=-. This stage in the process is purely classical, because energy scales below H correspond to scales outside the causal horizon, and so coherent quantum fluctuations do not contribute at these waveleng... |

37 |
A Covariant Entropy Conjecture,” JHEP 9907
- Bousso
- 1999
(Show Context)
Citation Context ...e obey cosmic no-hair theorem, and inflation will succeed in getting rid of initial inhomogeneities. This may be viewed as another example of the cosmological variant of the holographic principle [19]=-=[20]-=-. The structure of the spacetime is fully coded on the preferred screen, i.e. the apparent horizon. Its area is small during inflation because H must be large, and hence the Hubble region is censored ... |

29 |
Gluino condensation in strongly coupled heterotic string theory, Phys
- Horava
- 1996
(Show Context)
Citation Context ...e volume vanishes at the end of the interval where the hidden sector gauge group resides. One can then imagine strong coupling eects leading to supersymmetry breaking and the stabilization of moduli =-=[13,41]-=-. L11 determined this way depends on the topology of the E8E8 gaugeseld congurations on X, and on the Kahler moduli of X. For reasonable choices of both, L11 is consistent with (4.29). In this mode... |

25 |
Softly Broken Supersymmetry And SU(5)," Nucl. Phys
- Dimopoulos, Georgi
- 1981
(Show Context)
Citation Context ... two models we analyze – M-theory on X7 = X6 × S1 / Z2 [33], also known as Hoˇrava-Witten theory, and M-theory on a manifold of G2 holonomy – can be made consistent with the unification prediction of =-=[34]-=-, by keeping all scales including the eleven-dimensional Planck scale to within an order of magnitude of the unification scale, MGUT = 2×1016 GeV. In this case we will find that XH 2 /M 2 ∼ 10−7 , whi... |

19 |
Anomaly cancellation on G(2) manifolds,” hep-th/0108165
- Witten
(Show Context)
Citation Context .... Here, rather than having, roughly speaking, one large dimension as in the Hoˇrava-Witten case, we can have four large dimensions, as the singularities supporting gauge dynamics are codimension four =-=[14,15]-=-. If we abandon the requirement of precision grand unification and allow our compactification manifold to get as large as possible, while remaining consistent with the four dimensional character of in... |

17 |
Candidates For The Inflaton Field In Superstring Models,” Phys
- Binetruy, Gaillard
- 1986
(Show Context)
Citation Context ... the regime |η|, |ǫ| ≪ 1. The relative importance of these parameters depends on the model of inflation. For example, as we will see below in the case of natural inflation [17], or modular inflation, =-=[18]-=-, ǫ ≪ η. Thus the deviations from slow roll are mainly coded in the parameter η. In contrast, in the simplest model of chaotic inflation driven by a mass term, ǫ ∼ m2 /H2 >> η = 0 in the slow roll reg... |

17 |
Signature of Gravity Waves
- Seljak, Zaldarriaga
- 1997
(Show Context)
Citation Context ... we will be able to measure the B-mode of the CMB polarization to an accuracy limited only by cosmic variance. This gives a baseline in the spherical harmonic l from, say, l = 50 to l = 150 (see e.g. =-=[48]-=-). Given that the cosmic variance error in each point is ∼ √ l ∼ 10, and we have ∼ 100 points, we expect a precision of ∼ ±1%. We should emphasize again that this estimate is close to a best case scen... |

13 |
The Cosmic microwave background and particle physics
- Kamionkowski, Kosowsky
- 1999
(Show Context)
Citation Context ...3 In this case, the Hubble scale at inflation is, using the first of (2.25), (2.33) H ≃ 5.2 × 10 13 GeV , (2.34) which is within the bound allowed by COBE and large-scale structure measurements, c.f. =-=[28]-=-. The scale dependence is conveniently represented by defining the spectral index nS (or the tilt) and its gradient as For the modular inflation model we find δρ d ln ρ nS = 1 + 2 d lnk νS = dnS d lnk... |

10 |
et al., A preliminary measurement of the cosmic microwave background spectrum by the Cosmic Background Explorer (COBE) satellite
- Mather
- 1990
(Show Context)
Citation Context ...s proportional to (H/m4) 2 , where m4 is the (reduced) four dimensional Planck length. So measurements of this power give a direct measurement of 1 For textbook introductions see [1][2][3]. 1H. COBE =-=[6]-=- data already provide the interesting upper bound H < 10 14 GeV which corresponds to vacuum energies ∼ 10 16 GeV, the supersymmetric unification scale. Intensive efforts are under way to improve this ... |

10 | Short distance physics and the consistency relation for scalar and tensor fluctuations in the inflationary universe,” Phys.Rev. D65 - Hui, Kinney - 2002 |

9 |
et al., Constraints on Cosmological Parameters from MAXIMA-1, Astrophys
- Balbi
(Show Context)
Citation Context ... via its imprint on the cosmic microwave background radiation, δρ/ρ ∼ δT/T, thanks to the Sachs-Wolfe effect. This is directly measured by the COBE [6] satellite, and by the BOOMERanG [22] and MAXIMA =-=[23]-=- experiments, which set the normalization 7for the inhomogeneities at around δρ/ρ ∼ 10 −5 . They further observe that the spectrum of inhomogeneities is nearly scale-independent. To determine the imp... |

9 |
Particle Physics and Cosmology
- Linde
- 1990
(Show Context)
Citation Context ...he CMBR, whose power is proportional to (H=m4) 2, where m4 is the (reduced) four dimensional Planck length. So measurements of this power give a direct measurement of 1 For textbook introductions see =-=[1]-=-[2][3]. 1 H. COBE [6] data already provide the interesting upper bound H < 1014 GeV which corresponds to vacuum energies 1016 GeV, the supersymmetric unication scale. Intensive eorts are under way... |

7 |
Gluino condensation in strongly coupled heterotic string theory, Phys. Rev. D54
- Hoˇrava
- 1996
(Show Context)
Citation Context ... volume vanishes at the end of the interval where the hidden sector gauge group resides. One can then imagine strong coupling effects leading to supersymmetry breaking and the stabilization of moduli =-=[13,41]-=-. L11 determined this way depends on the topology of the E8 ×E8 gauge field configurations on X, and on the Kähler moduli of X. For reasonable choices of both, L11 is consistent with (4.29). In this m... |

6 |
Mass Scales Of The String Unification,” Phys
- Kaplunovsky
- 1985
(Show Context)
Citation Context ...lly viable string and M-theory models, the fundamental scale Mf – either the higherdimensional Planck scale or the string scale – is lower than the 4D Planck scale m4 by up to two orders of magnitude =-=[31,32,13]-=-. If we compactify a d-dimensional theory with Planck scale Mf on a (d−4)-dimensional manifold Xd−4 with volume Vd−4, then m 2 4 = Md−2 f Vd−4. The high scale m4 is not a dynamical scale, but rather a... |

6 | Baryogenesis in models with a low quantum gravity scale
- Benakli, Davidson
(Show Context)
Citation Context ...stabilized, and the effective 4D Planck scale is given by its low energy value m4 ≃ 2 × 10 18 GeV, if the vacuum energy is localized to the branes the Hubble scale H = m2 ∗ 3mPl,4 is incredibly small =-=[45]-=-, and the mass of the inflaton must be tiny [45],[46], sixteen orders of magnitude below m∗. In addition the effect, which is a correction on the order of H 2 /m 2 ∗ ∼ m2 ∗ /m2 Pl,4 to the inflaton fl... |

6 |
Inflation And Axion Cosmology,” Phys
- Linde
- 1987
(Show Context)
Citation Context ...onseld from CMBR data [4]. We should stress at this point that it is by no means necessary for the scale of in ation to be as high as H 1013 1014 GeV. Other in ationary models, e.g. hybrid models =-=[5]-=-, exist where H can be much lower, for example, H 103 GeV. Fortunately the scale of in ation can be experimentally tested. Since gravity couples to mass-energy, the amount of gravitational radiation... |

5 |
N=1 string duality,” Phys
- Harvey, Lowe, et al.
- 1995
(Show Context)
Citation Context ...olds with G2 holonomy also provide d = 4, N = 1 vacua. Few compact examples are known but one may appeal to heterotic-M theory duality in seven dimensions to make some arguments about their structure =-=[14,15]-=-. For another related construction see [43]. Calabi-Yau threefolds with geometric mirror partners are believed to be T 3 fibrations over an S 3 base [44]. Now heterotic string theory on T 3 is dual to... |

5 |
For reviews, see: (p
- Ge, Hu, et al.
- 1905
(Show Context)
Citation Context ...= 1 6π 2 M4 m4 V (2.21) 4 by slow roll equations (2.4). The tensor nature of these fluctuations induce oscillations in the plasma during decoupling which polarize the CMB photons in an observable way =-=[24]-=-. The ratio R = δ2 T /δ2 S is a characteristic of the inflationary model, and is given by R = 25 2 m 2 4[∂φV] 2 V 2 (2.22) It is straightforward to verify that in terms of the slow roll parameters, R ... |

5 |
Couplings and Scales in Superstring Models
- Dine, Seiberg
- 1985
(Show Context)
Citation Context ...lly viable string and M-theory models, the fundamental scale Mf { either the higherdimensional Planck scale or the string scale { is lower than the 4D Planck scale m4 by up to two orders of magnitude =-=[31,32,13]-=-. If we compactify a d-dimensional theory with Planck scale Mf on a (d4)-dimensional manifold Xd4 with volume Vd4, then m24 = Md2f Vd4. The high scale m4 is not a dynamical scale, but rather an a... |

5 | Remarks on M Theoretic Cosmology
- Banks
(Show Context)
Citation Context ...of time on them. In addition, in models which realize N = 1 supersymmetry, the explicit pattern of supersymmetry breaking means that moduli of the compactication manifold are good in aton candidates =-=[38,39]-=- as we will review below. If X10 = IR 4 X6 and X6 is Calabi-Yau, the theory has four unbroken supercharges in four dimensions. One E8 gauge multiplet is localized on each end of the interval. The gau... |

4 |
Probing Planckian Physics: Resonant
- Chung, Kolb, et al.
(Show Context)
Citation Context ... new physics via inflation. There have been a number of investigations of the signature of high energy scale physics in the CMBR. Heavy particles produced by parametric resonance have been studied in =-=[7]-=-. Several groups [8,9,10,11,12] have studied the effect that simple phenomenological models of stringy corrections to gravity would have on the inflationary fluctuation spectrum in the CMBR. This work... |

4 |
Inflation with a Planck scale frequency cutoff,” Phys
- Niemeyer
(Show Context)
Citation Context ...lation. There have been a number of investigations of the signature of high energy scale physics in the CMBR. Heavy particles produced by parametric resonance have been studied in [7]. Several groups =-=[8,9,10,11,12]-=- have studied the effect that simple phenomenological models of stringy corrections to gravity would have on the inflationary fluctuation spectrum in the CMBR. This work shares many features with the ... |

4 |
On the reliability of inflaton potential reconstruction, Phys. Rev. D58
- Copeland, Grivell, et al.
- 1998
(Show Context)
Citation Context ...evaluate ζ at the time the fluctuation exits the horizon; i.e., at momentum p = H. As pointed out in [25], if the slow roll approximation breaks down this procedure will not be accurate (however, see =-=[26]-=-). For the sake of simplicity we will restrict ourselves to models where this is not a concern. 8To compute the quantum fluctuation itself, one treats the fluctuating field as a perturbation around t... |

4 |
Starobinsky, Structure of primordial gravitational waves spectrum in a double inflationary model, Phys.Lett. B356
- Polarski, A
- 1995
(Show Context)
Citation Context ...ns in (4.1) lead to violations of (5.10), they are not the only possible source of such an effect. In particular, they are possible in theories with multiple scalar fields in addition to the inflaton =-=[49,50]-=-. Upon examining these models we find that appreciable effects require fine tuning of the scalar potential and the initial conditions for the scalar fields. In general these additional effects are pro... |

3 |
For a review see
- Lidsey
- 1997
(Show Context)
Citation Context ...spect. The first piece of high energy physics to be unraveled could well be dynamics of inflation itself. Much work has gone into how to reconstruct the potential of the inflaton field from CMBR data =-=[4]-=-. We should stress at this point that it is by no means necessary for the scale of inflation to be as high as H ∼ 1013 − 1014 GeV. Other inflationary models, e.g. hybrid models [5], exist where H can ... |

3 | Constraining inflation
- Adshead, Easther
- 2008
(Show Context)
Citation Context ...ur world appears to be local, this seems an excellent assumption. Perhaps we should phrase things in a more optimistic way. If experiments detect imprints in the CMBR of strength r .5 as predicted in =-=[11,12]-=- it would imply a breakdown of locality in low energy string theory, which might be a crucial clue in solving the cosmological constant problem! Alternatively, such results could also indicate that ph... |

3 |
Lange et al, Cosmological parameters from the first results of Boomerang, Phys
- E
(Show Context)
Citation Context ...d experimentally via its imprint on the cosmic microwave background radiation, δρ/ρ ∼ δT/T, thanks to the Sachs-Wolfe effect. This is directly measured by the COBE [6] satellite, and by the BOOMERanG =-=[22]-=- and MAXIMA [23] experiments, which set the normalization 7for the inhomogeneities at around δρ/ρ ∼ 10 −5 . They further observe that the spectrum of inhomogeneities is nearly scale-independent. To d... |

3 |
Cosmological In and Large-Scale Structure (Cambridge Univ
- Liddle, Lyth
- 2000
(Show Context)
Citation Context ...R, whose power is proportional to (H=m4) 2, where m4 is the (reduced) four dimensional Planck length. So measurements of this power give a direct measurement of 1 For textbook introductions see [1][2]=-=[3]-=-. 1 H. COBE [6] data already provide the interesting upper bound H < 1014 GeV which corresponds to vacuum energies 1016 GeV, the supersymmetric unication scale. Intensive eorts are under way to im... |

3 |
For a review see in
- Weisbuch, E
- 1995
(Show Context)
Citation Context ...ng prospect. Thesrst piece of high energy physics to be unraveled could well be dynamics of in ation itself. Much work has gone into how to reconstruct the potential of the in atonseld from CMBR data =-=[4]-=-. We should stress at this point that it is by no means necessary for the scale of in ation to be as high as H 1013 1014 GeV. Other in ationary models, e.g. hybrid models [5], exist where H can be... |

3 |
In and Large Internal Dimensions," Phys. Rev. D59
- Kaloper, Linde
- 1999
(Show Context)
Citation Context ...iven by its low energy value m4 ' 2 1018 GeV, if the vacuum energy is localized to the branes the Hubble scale H = m2 3mPl;4 is incredibly small [45], and the mass of the in aton must be tiny [45],=-=[46]-=-, sixteen orders of magnitude below m. In addition the eect, which is a correction on the order of H2=m2 m2=m2Pl;4 to the in atonsuctuation , is unobservable. However, it is inconsistent to se... |

2 |
Perturbation Spectrum
- Kempf, Niemeyer
(Show Context)
Citation Context ...lation. There have been a number of investigations of the signature of high energy scale physics in the CMBR. Heavy particles produced by parametric resonance have been studied in [7]. Several groups =-=[8,9,10,11,12]-=- have studied the effect that simple phenomenological models of stringy corrections to gravity would have on the inflationary fluctuation spectrum in the CMBR. This work shares many features with the ... |

2 |
Detectability of inflation produced gravitational waves,” Phys
- Turner
- 1997
(Show Context)
Citation Context ...in the future. Direct detection of relic gravitational waves (by more sensitive successors to LISA, for example) would probe short wavelengths and so would not be limited by cosmic variance (see e.g. =-=[51]-=-). Millisecond pulsar timing measurements would have the same advantage [52]. 9 Perhaps the most important lesson we have drawn from our work is a qualitative one: the idea of probing short distance p... |

2 |
One-Loop Four Graviton Amplitude
- Russo, Tseytlin
- 2000
(Show Context)
Citation Context ...aise this scale. We will take it to be the fundamental UV cutoff that quantum-mechanical M-theory is expected to provide. This cutoff can be estimated by studying four-graviton scattering at one loop =-=[39]-=-; since the amplitude is protected by supersymmetry, it can be calculated in string theory and extrapolated to strong coupling. The computation is cutoff dependent in supergravity. If we define the cu... |

1 |
Heterotic and Type I string dynamics form eleven dimensions", Nucl
- Horava, Witten
- 1996
(Show Context)
Citation Context ...e §4.1; they may then skip to §5 where the experimental consequences are discussed. Summary of results Our strategy will be as follows. The first two models we analyze – M-theory on X7 = X6 × S1 / Z2 =-=[33]-=-, also known as Hoˇrava-Witten theory, and M-theory on a manifold of G2 holonomy – can be made consistent with the unification prediction of [34], by keeping all scales including the eleven-dimensiona... |

1 |
Rapid Asymmetric Inflation and Early
- Arkani-Hamed, Dimopoulos, et al.
- 2000
(Show Context)
Citation Context ...46]. These problems are ameliorated if the extra dimensions play an active dynamical role in the early universe. Specifically, if the compactification volume was much smaller at the time of inflation =-=[47]-=-, the instantaneous Planck scale at the time of inflation was much smaller than its later value after the stabilization, implying that inflation at times before the extra dimensions are stabilized can... |

1 |
The Cosmic Gravitational Wave Background: Limits from Millisecond Pulsar Timing
- Stinebring, Ryba, et al.
- 1990
(Show Context)
Citation Context ...ive successors to LISA, for example) would probe short wavelengths and so would not be limited by cosmic variance (see e.g. [51]). Millisecond pulsar timing measurements would have the same advantage =-=[52]-=-. 9 Perhaps the most important lesson we have drawn from our work is a qualitative one: the idea of probing short distance physics using cosmological observations looks feasible, possibly even at ener... |

1 |
The Transplanckian Problem of In Cosmology," Phys. Rev. D63(2001) 123501, hep-th/0005209
- Martin, Brandenberger
(Show Context)
Citation Context ... ation. There have been a number of investigations of the signature of high energy scale physics in the CMBR. Heavy particles produced by parametric resonance have been studied in [7]. Several groups =-=[8,9,10,11,12]-=- have studied the eect that simple phenomenological models of stringy corrections to gravity would have on the in ationarysuctuation spectrum in the CMBR. This work shares many features with the resu... |

1 |
In With a Planck Scale Frequency Cuto," Phys. Rev
- Niemeyer
- 2001
(Show Context)
Citation Context ... ation. There have been a number of investigations of the signature of high energy scale physics in the CMBR. Heavy particles produced by parametric resonance have been studied in [7]. Several groups =-=[8,9,10,11,12]-=- have studied the eect that simple phenomenological models of stringy corrections to gravity would have on the in ationarysuctuation spectrum in the CMBR. This work shares many features with the resu... |

1 |
Natural In with Pseudo-NambuGoldstone Bosons
- Freese, Frieman, et al.
- 1990
(Show Context)
Citation Context ...ion is then formally dened as the regime jj; jj 1. The relative importance of these parameters depends on the model of in ation. For example, as we will see below in the case of natural in ation =-=[17]-=-, or modular in ation, [18], . Thus the deviations from slow roll are mainly coded in the parameter . In contrast, in the simplest model of chaotic in ation driven by a mass term, m2=H2 >> ... |

1 |
Candidates for the In Field in Superstring Models," Phys. Rev. D34
- Binetruy, Gaillard
- 1986
(Show Context)
Citation Context ... as the regime jj; jj 1. The relative importance of these parameters depends on the model of in ation. For example, as we will see below in the case of natural in ation [17], or modular in ation, =-=[18]-=-, . Thus the deviations from slow roll are mainly coded in the parameter . In contrast, in the simplest model of chaotic in ation driven by a mass term, m2=H2 >> = 0 in the slow roll regim... |

1 |
On the Problem of Predicting In Perturbations," Phys. Lett. B414
- Wang, Mukhanov, et al.
- 1997
(Show Context)
Citation Context ...therefore to compute the quantumsuctuation of the in atonseld in de Sitter space, and then use it to evaluate at the time thesuctuation exits the horizon; i.e., at momentum p = H. As pointed out in =-=[25]-=-, if the slow roll approximation breaks down this procedure will not be accurate (however, see [26]). For the sake of simplicity we will restrict ourselves to models where this is not a concern. 8 To ... |

1 |
Chaotic In
- Linde
- 1983
(Show Context)
Citation Context ...e them henceforth. 16 In some cases, most of the late in ationary expansion can occur during thesnal approach of the in aton to the minimum of the potential; this the the scenario of chaotic in ation =-=[29]-=-. In these cases, the potential is V = n n; (2:44) where V is the dimensionful quantity V = M4V. In the slow roll approximation theseld equations reduce to H = r 3n n=2 m4 _ = r n 3 m4 n=2... |

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Mass Scales of the String Uni
- Kaplunovsky
- 1985
(Show Context)
Citation Context ...lly viable string and M-theory models, the fundamental scale Mf { either the higherdimensional Planck scale or the string scale { is lower than the 4D Planck scale m4 by up to two orders of magnitude =-=[31,32,13]-=-. If we compactify a d-dimensional theory with Planck scale Mf on a (d4)-dimensional manifold Xd4 with volume Vd4, then m24 = Md2f Vd4. The high scale m4 is not a dynamical scale, but rather an a... |

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One-loop Four-graviton Amplitude in Eleven-Dimensional Supergravity," Nuc. Phys. B508
- Lett
- 1997
(Show Context)
Citation Context ... raise this scale. We will take it to be the fundamental UV cuto that quantum-mechanical M-theory is expected to provide. This cuto can be estimated by studying four-graviton scattering at one loop =-=[42]-=-; since the amplitude is protected by supersymmetry, it can be calculated in string theory and extrapolated to strong coupling. The computation is cuto dependent in supergravity. If we dene the cuto... |

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Rapid Asymmetric In and Early Cosmology in Theories with Sub-millimeter Dimensions," Nucl. Phys. B567
- Arkani-Hamed, Dimopoulos, et al.
- 2000
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Citation Context ...s [46]. These problems are ameliorated if the extra dimensions play an active dynamical role in the early universe. Specically, if the compactication volume was much smaller at the time of in ation =-=[47]-=-, the instantaneous Planck scale at the time of in ation was much smaller than its later value after the stabilization, implying that in ation at times before the extra dimensions are stabilized can a... |

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Adiabatic and Isocurvature Perturbations from In Power Spectra and Consistency Relations," Phys. Rev. D64
- Bartolo, Matarrese, et al.
- 2001
(Show Context)
Citation Context ...ctions in (4.1) lead to violations of (5.10), they are not the only possible source of such an eect. In particular, they are possible in theories with multiple scalarselds in addition to the in aton =-=[49,50]-=-. Upon examining these models wesnd that appreciable eects requiresne tuning of the scalar potential and the initial conditions for the scalarselds. In general these additional eects are probably un... |

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Detectability of In Produced Gravitational Waves," Phys. Rev. D55
- Turner
- 1997
(Show Context)
Citation Context ...in the future. Direct detection of relic gravitational waves (by more sensitive successors to LISA, for example) would probe short wavelengths and so would not be limited by cosmic variance (see e.g. =-=[51]-=-). Millisecond pulsar timing measurements would have the same advantage [52]. 9 Perhaps the most important lesson we have drawn from our work is a qualitative one: the idea of probing short distance p... |