arXiv subjects

Paolo Creminelli

Publications and source records attributed to Paolo Creminelli.

At least 37 records · Page 2Linked to original sources

arXiv2017

Simplifying the EFT of Inflation: Generalized Disformal Transformations and Redundant Couplings

We study generalized disformal transformations, including derivatives of the metric, in the context of the Effective Field Theory of Inflation. All these transformations do not change the late-time cosmological observables but change the coefficients of the operators in the action: some couplings are effectively redundant. At leading order in derivatives and up to cubic order in perturbations, one has 6 free functions that can be used to set to zero 6 of the 17 operators at this order. This is used to show that the tensor three-point function cannot be modified at leading order in derivatives, while the scalar-tensor-tensor correlator can only be modified by changing the scalar dynamics. At higher order in derivatives there are transformations that do not affect the Einstein-Hilbert action: one can find 6 additional transformations that can be used to simplify the inflaton action, at least when the dynamics is dominated by the lowest derivative terms. We also identify the leading higher-derivative corrections to the tensor power spectrum and bispectrum.

astro-ph.CO↗

arXiv2017

Solid Consistency

We argue that $isotropic$ scalar fluctuations in solid inflation are adiabatic in the super-horizon limit. During the solid phase this adiabatic mode has peculiar features: constant energy-density slices and comoving slices do not coincide, and their curvatures, parameterized respectively by $ζ$ and $\mathcal R$, both evolve in time. The existence of this adiabatic mode implies that Maldacena's squeezed limit consistency relation holds after angular average over the long mode. The correlation functions of a long-wavelength spherical scalar mode with several short scalar or tensor modes is fixed by the scaling behavior of the correlators of short modes, independently of the solid inflation action or dynamics of reheating.

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arXiv2016

Relaxing the Cosmological Constant: a Proof of Concept

We propose a technically natural scenario whereby an initially large cosmological constant (c.c.) is relaxed down to the observed value due to the dynamics of a scalar evolving on a very shallow potential. The model crucially relies on a sector that violates the null energy condition (NEC) and gets activated only when the Hubble rate becomes sufficiently small --- of the order of the present one. As a result of NEC violation, this low-energy universe evolves into inflation, followed by reheating and the standard Big Bang cosmology. The symmetries of the theory force the c.c. to be the same before and after the NEC-violating phase, so that a late-time observer sees an effective c.c. of the correct magnitude. Importantly, our model allows neither for eternal inflation nor for a set of possible values of dark energy, the latter fixed by the parameters of the theory.

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arXiv2016

Stability of Geodesically Complete Cosmologies

We study the stability of spatially flat FRW solutions which are geodesically complete, i.e. for which one can follow null (graviton) geodesics both in the past and in the future without ever encountering singularities. This is the case of NEC-violating cosmologies such as smooth bounces or solutions which approach Minkowski in the past. We study the EFT of linear perturbations around a solution of this kind, including the possibility of multiple fields and fluids. One generally faces a gradient instability which can be avoided only if the operator $~^{(3)}{R} δN~$ is present and its coefficient changes sign along the evolution. This operator (typical of beyond-Horndeski theories) does not lead to extra degrees of freedom, but cannot arise starting from any theory with second-order equations of motion. The change of sign of this operator prevents to set it to zero with a generalised disformal transformation.

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arXiv2016

Tensor Squeezed Limits and the Higuchi Bound

We point out that tensor consistency relations-i.e. the behavior of primordial correlation functions in the limit a tensor mode has a small momentum-are more universal than scalar consistency relations. They hold in the presence of multiple scalar fields and as long as anisotropies are diluted exponentially fast. When de Sitter isometries are approximately respected during inflation this is guaranteed by the Higuchi bound, which forbids the existence of light particles with spin: De Sitter space can support scalar hair but no curly hair. We discuss two indirect ways to look for the violation of tensor con- sistency relations in observations, as a signature of models in which inflation is not a strong isotropic attractor, such as solid inflation: (a) Graviton exchange contribution to the scalar four-point function; (b) Quadrupolar anisotropy of the scalar power spectrum due to super-horizon tensor modes. This anisotropy has a well-defined statistics which can be distinguished from cases in which the background has a privileged direction.

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arXiv2016

Inequivalence of Coset Constructions for Spacetime Symmetries: Coupling with Gravity

We study how the coupling with gravity of theories with non-linearly realized space-time symmetries is modified when one changes the parametrization of the coset. As an example, we focus on the so-called Galileon duality: a reparametrization which maps a Galilean invariant action into another one which enjoys the same symmetry. Starting with a standard coupling with gravity, with a parametric separation between the Planck scale and the typical scale of the coset, one ends up with a theory without such a separation. In particular an infinite set of higher-dimension operators are relevant when the superluminality of the Galileon is measurable in the effective theory. This addresses an apparent paradox since superluminality arises in the dual theory even when absent in the original one.

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arXiv2015

Implications of the scalar tilt for the tensor-to-scalar ratio

We investigate the possible implications of the measured value of the scalar tilt $n_s$ for the tensor-to-scalar ratio $r$ in slow-roll, single-field inflationary models. The measured value of the tilt satisfies $n_s -1\sim 1/N_*$, where $N_* \sim 60$ is the number of $e$-folds for observationally relevant scales. If this is not a coincidence and the scaling holds for different values of $N$, it strongly suggests that either $r$ is as big as $10^{-1}$ (a possibility in tension with the recent data), or smaller than $10^{-2}$ and exponentially dependent on $n_s$. A large region of the ($n_s$,$r$) plane is not compatible with this scaling.

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arXiv2015

Detecting Primordial $B$-Modes after Planck

We update the forecasts for the measurement of the tensor-to-scalar ratio $r$ for various ground-based experiments (AdvACT, CLASS, Keck/BICEP3, Simons Array, SPT-3G), balloons (EBEX 10k and Spider) and satellites (CMBPol, COrE and LiteBIRD), taking into account the recent Planck data on polarized dust and using a component separation method. The forecasts do not change significantly with respect to previous estimates when at least three frequencies are available, provided foregrounds can be accurately described by few parameters. We argue that a theoretically motivated goal for future experiments is $r\sim2\times10^{-3}$, and that this is achievable if the noise is reduced to $\sim1\,μ$K-arcmin and lensing is reduced to $10\%$ in power. We study the constraints experiments will be able to put on the frequency and $\ell$-dependence of the tensor signal as a check of its primordial origin. Futuristic ground-based and balloon experiments can have good constraints on these parameters, even for $r\sim2\times10^{-3}$. For the same value of $r$, satellites will marginally be able to detect the presence of the recombination bump, the most distinctive feature of the primordial signal.

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arXiv2015

Inequivalence of Coset Constructions for Spacetime Symmetries

Non-linear realizations of spacetime symmetries can be obtained by a generalization of the coset construction valid for internal ones. The physical equivalence of different representations for spacetime symmetries is not obvious, since their relation involves not only a redefinition of the fields but also a field-dependent change of coordinates. A simple and relevant spacetime symmetry is obtained by the contraction of the 4D conformal group that leads to the Galileon group. We analyze two non-linear realizations of this group, focusing in particular on the propagation of signals around non-trivial backgrounds. The aperture of the lightcone is in general different in the two representations and in particular a free (luminal) massless scalar is mapped in a Galileon theory which admits superluminal propagation. We show that in this theory, if we consider backgrounds that vanish at infinity, there is no asymptotic effect: the displacement of the trajectory integrates to zero, as can be expected since the S-matrix is trivial. Regarding local measurements, we show that the puzzle is solved taking into account that a local coupling with fixed sources in one theory is mapped into a non-local coupling and we show that this effect compensates the different lightcone. Therefore the two theories have a different notion of locality. The same applies to the different non-linear realizations of the conformal group and we study the particular case of a cosmologically interesting background: the Galilean Genesis scenarios.

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arXiv2014

Resilience of the standard predictions for primordial tensor modes

We show that the prediction for the primordial tensor power spectrum cannot be modified at leading order in derivatives. Indeed, one can always set to unity the speed of propagation of gravitational waves during inflation by a suitable disformal transformation of the metric, while a conformal one can make the Planck mass time-independent. Therefore, the tensor amplitude unambiguously fixes the energy scale of inflation. Using the Effective Field Theory of Inflation, we check that predictions are independent of the choice of frame, as expected. The first corrections to the standard prediction come from two parity violating operators with three derivatives. Also the correlator $<γγγ>$ is standard and only receives higher derivative corrections. These results hold also in multifield models of inflation and in alternatives to inflation and make the connection between a (quasi) scale-invariant tensor spectrum and inflation completely robust.

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arXiv2014

Single-Field Consistency Relations of Large Scale Structure. Part III: Test of the Equivalence Principle

The recently derived consistency relations for Large Scale Structure do not hold if the Equivalence Principle (EP) is violated. We show it explicitly in a toy model with two fluids, one of which is coupled to a fifth force. We explore the constraints that galaxy surveys can set on EP violation looking at the squeezed limit of the 3-point function involving two populations of objects. We find that one can explore EP violations of order 10^{-3} - 10^{-4} on cosmological scales. Chameleon models are already very constrained by the requirement of screening within the Solar System and only a very tiny region of the parameter space can be explored with this method. We show that no violation of the consistency relations is expected in Galileon models.

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arXiv2014

$ϕ^2$ or Not $ϕ^2$: Testing the Simplest Inflationary Potential

The simplest inflationary model $V=\frac12 m^2ϕ^2$ represents the benchmark for future constraints. For a quadratic potential, the quantity $(n_s-1)+r/4+11 (n_s-1)^2/24$ vanishes (up to corrections which are cubic in slow roll) and can be used to parametrize small deviations from the minimal scenario. Future constraints on this quantity will be able to distinguish a quadratic potential from a pseudo-Nambu-Goldstone boson with $f \lesssim 30 M_{\rm pl}$ and set limits on the deviation from unity of the speed of sound $| c_s-1| \lesssim 3\times 10^{-2}$ (corresponding to an energy scale $Λ\gtrsim 2\times 10^{16}\, \mathrm{GeV}$), and on the contribution of a second field to perturbations ($\lesssim 6 \times 10^{-2}$). The limiting factor for these bounds will be the uncertainty on the spectral index. The error on the number of e-folds will be $ΔN \simeq 0.4$, corresponding to an error on the reheating temperature $ΔT_\mathrm{rh}/T_\mathrm{rh}\simeq 1.2$. We comment on the relevance of non-Gaussianity after BICEP2 results.

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arXiv2014

$ϕ^2$ Inflation at its Endpoint

In the simplest inflationary model $V=\frac12 m^2ϕ^2$, we provide a prediction accurate up to $1\%$ for the spectral index $n_s$ and the tensor-to-scalar ratio $r$ assuming instantaneous reheating and a standard thermal history: $n_s = 0.9668\pm0.0003$ and $r=0.131\pm 0.001$. This represents the simplest and most informative point in the $(n_s,r)$ plane. The result is independent of the details of reheating (or preheating) provided the conversion to radiation is sufficiently fast. A slower reheating or a modified post-inflationary evolution push towards smaller $n_s$ (and larger $r$), so that our prediction corresponds to the maximum $n_s$ (and minimum $r$) for the quadratic potential. We also derive similar results for a general $V \propto ϕ^p$ potential.

astro-ph.CO↗

arXiv2014

Single-Field Consistency Relations of Large Scale Structure. Part II: Resummation and Redshift Space

We generalize the recently derived single-field consistency relations of Large Scale Structure in two directions. First, we treat the effect of the long modes (with momentum q) on the short ones (with momentum k) non-perturbatively, by writing resummed consistency relations which do not require k/q δ_q << 1. These relations do not make any assumptions on the short-scales physics and are extended to include (an arbitrary number of) multiple long modes, internal lines with soft momenta and soft loops. We do several checks of these relations in perturbation theory and we verify that the effect of soft modes always cancels out in equal-time correlators. Second, we write the relations directly in redshift space, without assuming the single-stream approximation: not only the long mode affects the short scales as a homogeneous gravitational field, but it also displaces them by its velocity along the line-of-sight. Redshift space consistency relations still vanish when short modes are taken at equal time: an observation of a signal in the squeezed limit would point towards multifield inflation or a violation of the equivalence principle.

astro-ph.CO↗

arXiv2014

ISO(4,1) Symmetry in the EFT of Inflation

In DBI inflation the cubic action is a particular linear combination of the two, otherwise independent, cubic operators \dot π^3 and \dot π(\partial_i π)^2. We show that in the Effective Field Theory (EFT) of inflation this is a consequence of an approximate 5D Poincaré symmetry, ISO(4,1), non-linearly realized by the Goldstone π. This symmetry uniquely fixes, at lowest order in derivatives, all correlation functions in terms of the speed of sound c_s. In the limit c_s \to 1, the ISO(4,1) symmetry reduces to the Galilean symmetry acting on π. On the other hand, we point out that the non-linear realization of SO(4,2), the isometry group of 5D AdS space, does not fix the cubic action in terms of c_s.

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arXiv2014

Single-Field Consistency Relations of Large Scale Structure

We derive consistency relations for the late universe (CDM and ΛCDM): relations between an n-point function of the density contrast δand an (n+1)-point function in the limit in which one of the (n+1) momenta becomes much smaller than the others. These are based on the observation that a long mode, in single-field models of inflation, reduces to a diffeomorphism since its freezing during inflation all the way until the late universe, even when the long mode is inside the horizon (but out of the sound horizon). These results are derived in Newtonian gauge, at first and second order in the small momentum q of the long mode and they are valid non-perturbatively in the short-scale δ. In the non-relativistic limit our results match with (Kehagias and Riotto '13) and (Peloso and Pietroni '13). These relations are a consequence of diffeomorphism invariance; they are not satisfied in the presence of extra degrees of freedom during inflation or violation of the Equivalence Principle (extra forces) in the late universe.

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arXiv2013

The Physical Squeezed Limit: Consistency Relations at Order q^2

In single-field models of inflation the effect of a long mode with momentum q reduces to a diffeomorphism at zeroth and first order in q. This gives the well-known consistency relations for the n-point functions. At order q^2 the long mode has a physical effect on the short ones, since it induces curvature, and we expect that this effect is the same as being in a curved FRW universe. In this paper we verify this intuition in various examples of the three-point function, whose behaviour at order q^2 can be written in terms of the power spectrum in a curved universe. This gives a simple alternative understanding of the level of non-Gaussianity in single-field models. Non-Gaussianity is always parametrically enhanced when modes freeze at a physical scale k_{ph, f} shorter than H: f_{NL} \sim (k_{ph, f}/H)^2.

astro-ph.CO↗

arXiv2013

Non-linear Representations of the Conformal Group and Mapping of Galileons

There are two common non-linear realizations of the 4D conformal group: in the first, the dilaton is the conformal factor of the effective metric η_{μν} e^{-2 π}; in the second it describes the fluctuations of a brane in AdS_5. The two are related by a complicated field redefinition, found by Bellucci, Ivanov and Krivonos (2002) to all orders in derivatives. We show that this field redefinition can be understood geometrically as a change of coordinates in AdS_5. In one gauge the brane is rigid at a fixed radial coordinate with a conformal factor on the AdS_5 boundary, while in the other one the brane bends in an unperturbed AdS_5. This geometrical picture illuminates some aspects of the mapping between the two representations. We show that the conformal Galileons in the two representations are mapped into each other in a quite non-trivial way: the DBI action, for example, is mapped into a complete linear combination of all the five Galileons in the other representation. We also verify the equivalence of the dilaton S-matrix in the two representations and point out that the aperture of the dilaton light-cone around non-trivial backgrounds is not the same in the two representations.

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