arXiv subjects

Subodh P. Patil

Publications and source records attributed to Subodh P. Patil.

At least 37 records · Page 2Linked to original sources

arXiv2019

Reconstructing the EFT of Inflation from Cosmological Data

Reconstructions of the primordial power spectrum (PPS) of curvature perturbations from cosmic microwave background anisotropies and large-scale structure data suggest that the usually assumed power-law PPS has localised features (up to $\sim 10\%$ in amplitude), although of only marginal significance in the framework of $Λ$CDM cosmology. On the other hand if the underlying cosmology is assumed to be Einstein-de Sitter, larger features in the PPS (up to $\sim 20\%$) are required to accurately fit the observed acoustic peaks. Within the context of single clock inflation, we show that any given reconstruction of the PPS can be mapped on to functional parameters of the underlying effective theory of the adiabatic mode within a 2nd-order formalism, provided the best fit fractional change of the PPS, $Δ\mathcal{P}_\mathcal{R}/\mathcal{P}_\mathcal{R}$ is such that $(Δ\mathcal{P}_\mathcal{R}/\mathcal{P}_\mathcal{R})^3$ falls within the $1\,σ$ confidence interval of the reconstruction for features induced by variations of either the sound speed $c_\mathrm{s}$ or the slow-roll parameter $ε$. Although there is a degeneracy amongst these functional parameters (and the models that project onto them), we can identify simple representative inflationary models that yield such features in the PPS. Thus we provide a dictionary (more accurately, a thesaurus) to go from observational data, via the reconstructed PPS, to models that reproduce them to per cent level precision.

astro-ph.CO↗

arXiv2019

Steepest growth of the power spectrum and primordial black holes

We derive analytic bounds on the shape of the primordial power spectrum in the context of single-field inflation. In particular, the steepest possible growth has a spectral index of $n_s - 1 = 4$ once transients have died down. Its primary implication is that any constraint on the power spectrum at a particular scale can be extrapolated to an upper bound over an extended range of scales. This is important for models which generate relics due to an enhanced amplitude of the primordial scalar perturbations, such as primordial black holes. In order to generate them, the power spectrum needs to grow many orders of magnitude larger than its observed value on CMB scales - typically achieved through a phase of ultra slow-roll inflation - and is thus subject to additional constraints at small scales. We plot all relevant constraints including CMB spectral distortions and gravitational waves sourced by scalar perturbations at second order. We show how this limits the allowed mass of PBHs, especially for the large masses of interest following recent detections by LIGO and prospects for constraining them further with future observations. We show that any transition from approximately constant $ε$ slow-roll inflation to a phase where the power spectrum rapidly rises necessarily implies an intervening dip in power. We also show how to reconstruct a potential that can reproduce an arbitrary time-varying $ε$, offering a complementary perspective on how ultra slow-roll can be achieved.

astro-ph.CO↗

arXiv2018

Tensor Bounds on the Hidden Universe

During single clock inflation, hidden fields (i.e. fields coupled to the inflaton only gravitationally) in their adiabatic vacua can ordinarily only affect observables through virtual effects. After renormalizing background quantities (fixed by observations at some pivot scale), all that remains are logarithmic runnings in correlation functions that are both Planck and slow roll suppressed. In this paper we show how a large number of hidden fields can partially compensate this suppression and generate a potentially observable running in the tensor two point function, consistently inferable courtesy of a large $N$ resummation. We detour to address certain subtleties regarding loop corrections during inflation, extending the analysis of [1]. Our main result is that one can extract bounds on the hidden field content of the universe from bounds on violations of the consistency relation between the tensor spectral index and the tensor to scalar ratio, were primordial tensors ever detected. Such bounds are more competitive than the naive bound inferred from requiring inflation to occur below the strong coupling scale of gravity if deviations from the consistency relation can be bounded to within the sub-percent level. We discuss how one can meaningfully constrain the parameter space of various phenomenological scenarios and constructions that address naturalness with a large number of species (such as `N-naturalness') with CMB observations up to cosmic variance limits, and possibly future 21cm and gravitational wave observations.

gr-qc↗

arXiv2018

Renormalization of Sparse Disorder in the Ising Model

We consider the renormalization of quenched bond disorder in the Ising model in the limit that it is sparse -- highly localized and vanishing in the thermodynamic limit. We begin in 1D with arbitrary disorder assigned to a finite number of bonds and study how the system renormalizes, finding non-trivial fixed point structure for any given bond with a separatrix at zero bond strength, equivalent to inserting a break in the chain. Either side of this critical line, renormalization group (RG) trajectories flow towards one of two attractors on which the disordered bonds settle onto ferromagnetic or anti-ferromagnetic (AF) couplings of equal and opposite magnitude. Bonds that settle on an AF attractor are equivalent to inserting a twist in the chain at the location of the bond, implying a multi-kink ground state solution. Qualitatively different behavior emerges at the RG step when bonds start to coalesce, with the chain `untwisting' whenever two AF bonds coalesce. Our findings generalize to higher dimensions for codimension one defects that are sparse from the perspective of the orthogonal complement lattice. In 2D, the $\mathbb Z_2$ symmetry of the model has an IR manifestation where one can construct field strengths and Wilson loops (which characterize frustration) from fundamental plaquette variables. In the non-sparse limit where the disorder parameter is drawn from an arbitrary but homogeneously assigned probability distribution function, we recover previously found fixed distributions as special cases, but find only the trivial paramagnetic distribution to be an attractor. For non-homogeneously assigned disorder that is sufficiently dilute however, we find the Edwards-Anderson model with equal probability $\pm J$ bonds to also be an IR attractor.

cond-mat.stat-mech↗

arXiv2017

Damping of gravitational waves by matter

We develop a unified description, via the Boltzmann equation, of damping of gravitational waves by matter, incorporating collisions. We identify two physically distinct damping mechanisms -- collisional and Landau damping. We first consider damping in flat spacetime, and then generalize the results to allow for cosmological expansion. In the first regime, maximal collisional damping of a gravitational wave, independent of the details of the collisions in the matter is, as we show, significant only when its wavelength is comparable to the size of the horizon. Thus damping by intergalactic or interstellar matter for all but primordial gravitational radiation can be neglected. Although collisions in matter lead to a shear viscosity, they also act to erase anisotropic stresses, thus suppressing the damping of gravitational waves. Damping of primordial gravitational waves remains possible. We generalize Weinberg's calculation of gravitational wave damping, now including collisions and particles of finite mass, and interpret the collisionless limit in terms of Landau damping. While Landau damping of gravitational waves cannot occur in flat spacetime, the expansion of the universe allows such damping by spreading the frequency of a gravitational wave of given wavevector.

gr-qc↗

arXiv2016

Goldilocks Models of Higher-Dimensional Inflation (including modulus stabilization)

We explore the mechanics of inflation in simplified extra-dimensional models involving an inflaton interacting with the Einstein-Maxwell system in two extra dimensions. The models are Goldilocks-like in that they are just complicated enough to include a mechanism to stabilize the extra-dimensional size, yet simple enough to solve the full 6D field equations using basic tools. The solutions are not limited to the effective 4D regime with H << m_KK (the latter referring to the mass splitting of the Kaluza-Klein excitations) because the full 6D Einstein equations are solved. This allows an exploration of inflationary physics in a controlled regime away from the usual 4D lamp-post. The inclusion of modulus stabilization is important as experience with string models teaches that this is usually what makes models fail: stabilization energies dominate the shallow potentials required by slow roll and open up directions to evolve that are steeper than those of the putative inflationary direction. We explore three representative inflationary scenarios within this simple setup. In one the radion is trapped in an inflaton-dependent local minimum whose non-zero energy drives inflation. Inflation ends as this energy relaxes to zero when the inflaton finds its minimum. The others involve power-law solutions during inflation. One is an attractor whose features are relatively insensitive to initial conditions but whose slow-roll parameters cannot be arbitrarily small; the other is not an attractor but can roll much more slowly, until eventually decaying to the attractor. These solutions can satisfy H > m_KK, but when they do standard 4D fluctuation calculations need not apply. When in a 4D regime the solutions predict eta ~ 0 hence r ~ 0.11 when n_s ~ 0.96 and so are ruled out if tensor modes remain unseen. Analysis of general parameters is difficult without a full 6D fluctuation calculation.

gr-qc↗

arXiv2016

Relaxing the Electroweak Scale: the Role of Broken dS Symmetry

Recently, a novel mechanism to address the hierarchy problem has been proposed \cite{Graham:2015cka}, where the hierarchy between weak scale physics and any putative `cutoff' $M$ is translated into a parametrically large field excursion for the so-called relaxion field, driving the Higgs mass to values much less than $M$ through cosmological dynamics. In its simplest incarnation, the relaxion mechanism requires nothing beyond the standard model other than an axion (the relaxion field) and an inflaton. In this note, we critically re-examine the requirements for successfully realizing the relaxion mechanism and point out that parametrically larger field excursions can be obtained for a given number of e-folds by simply requiring that the background break exact de Sitter invariance. We discuss several corollaries of this observation, including the interplay between the upper bound on the scale $M$ and the order parameter $ε$ associated with the breaking of dS symmetry, and entertain the possibility that the relaxion could play the role of a curvaton. We find that a successful realization of the mechanism is possible with as few as $\mathcal O (10^3)$ e-foldings, albeit with a reduced cutoff $M \sim 10^6$ GeV for a dark QCD axion and outline a minimal scenario that can be made consistent with CMB observations.

hep-ph↗

arXiv2015

The Effective Strength of Gravity, the Scale of Inflation (and how KK gravitons evade the Higuchi Bound)

For any given momentum transfer, gravitational interactions have a strength set by a characteristic scale $M_*$ inferred from amplitudes calculated in an effective theory with a strong coupling scale $M_{**}$. These are in general different from each other and $M_{\rm pl}$, the macroscopic strength of gravity as determined by (laboratory scale) Cavendish experiments. During single field inflation, $M_*$ can differ from $M_{\rm pl}$ due to the presence of any number of (hidden) universally coupled species between laboratory and inflationary scales. Although this has no effect on dimensionless (i.e. observable) quantities measured at a fixed scale such as the amplitude and spectral properties of the CMB anisotropies, it complicates the inference of an absolute scale of inflation given any detection of primordial tensors. In this note we review and elaborate upon these facts and address concerns raised in a recent paper.

hep-th↗

arXiv2015

On the Predictiveness of Single-Field Inflationary Models

We re-examine the predictiveness of single-field inflationary models and discuss how an unknown UV completion can complicate determining inflationary model parameters from observations, even from precision measurements. Besides the usual naturalness issues associated with having a shallow inflationary potential, we describe another issue for inflation, namely, unknown UV physics modifies the running of Standard Model (SM) parameters and thereby introduces uncertainty into the potential inflationary predictions. We illustrate this point using the minimal Higgs Inflationary scenario, which is arguably the most predictive single-field model on the market, because its predictions for $A_s$, $r$ and $n_s$ are made using only one new free parameter beyond those measured in particle physics experiments, and run up to the inflationary regime. We find that this issue can already have observable effects. At the same time, this UV-parameter dependence in the Renormalization Group allows Higgs Inflation to occur (in principle) for a slightly larger range of Higgs masses. We comment on the origin of the various UV scales that arise at large field values for the SM Higgs, clarifying cut off scale arguments by further developing the formalism of a non-linear realization of $\rm SU_L(2) \times U(1)$ in curved space. We discuss the interesting fact that, outside of Higgs Inflation, the effect of a non-minimal coupling to gravity, even in the SM, results in a non-linear EFT for the Higgs sector. Finally, we briefly comment on post BICEP2 attempts to modify the Higgs Inflation scenario.

hep-ph↗

arXiv2015

Features and New Physical Scales in Primordial Observables: Theory and Observation

All cosmological observations to date are consistent with adiabatic, Gaussian and nearly scale invariant initial conditions. These findings provide strong evidence for a particular symmetry breaking pattern in the very early universe (with a close to vanishing order parameter, $ε$), widely accepted as conforming to the predictions of the simplest realizations of the inflationary paradigm. However, given that our observations are only privy to perturbations, in inferring something about the background that gave rise to them, it should be clear that many different underlying constructions project onto the same set of cosmological observables. Features in the primordial correlation functions, if present, would offer a unique and discriminating window onto the parent theory in which the mechanism that generated the initial conditions is embedded. In certain contexts, simple linear response theory allows us to infer new characteristic scales from the presence of features that can break the aforementioned degeneracies among different background models, and in some cases can even offer a limited spectroscopy of the heavier degrees of freedom that couple to the inflaton. In this review, we offer a pedagogical survey of the diverse, theoretically well grounded mechanisms which can imprint features into primordial correlation functions in addition to reviewing the techniques one can employ to probe observations. These observations include cosmic microwave background anisotropies and spectral distortions as well as the matter two and three point functions as inferred from large-scale structure and potentially, 21 cm surveys.

astro-ph.CO↗

arXiv2015

The Effective Planck Mass and the Scale of Inflation

Observable quantities in cosmology are dimensionless, and therefore independent of the units in which they are measured. This is true of all physical quantities associated with the primordial perturbations that source cosmic microwave background anisotropies such as their amplitude and spectral properties. However, if one were to try and infer an absolute energy scale for inflation-- a priori, one of the more immediate corollaries of detecting primordial tensor modes-- one necessarily makes reference to a particular choice of units, the natural choice for which is Planck units. In this note, we discuss various aspects of how inferring the energy scale of inflation is complicated by the fact that the effective strength of gravity as seen by inflationary quanta necessarily differs from that seen by gravitational experiments at presently accessible scales. The uncertainty in the former relative to the latter has to do with the unknown spectrum of universally coupled particles between laboratory scales and the putative scale of inflation. These intermediate particles could be in hidden as well as visible sectors or could also be associated with Kaluza-Klein resonances associated with a compactification scale below the scale of inflation. We discuss various implications for cosmological observables.

hep-th↗

arXiv2014

Closed String Thermodynamics and a Blue Tensor Spectrum

The BICEP-2 team has reported the detection of primordial cosmic microwave background B-mode polarization, with hints of a suppression of power at large angular scales relative to smaller scales. Provided that the B-mode polarization is due to primordial gravitational waves, this might imply a blue tilt of the primordial gravitational wave spectrum. Such a tilt would be incompatible with standard inflationary models, although it was predicted some years ago in the context of a mechanism that thermally generates the primordial perturbations through a Hagedorn phase of string cosmology. The purpose of this note is to encourage greater scrutiny of the data with priors informed by a model that is immediately falsifiable, but which \textit{predicts} features that might be favoured by the data-- namely a blue tensor tilt with an induced and complimentary red tilt to the scalar spectrum, with a naturally large tensor to scalar ratio that relates to both.

astro-ph.CO↗

arXiv2014

Cosmological Perturbations Across an S-brane

Space-filling S-branes can mediate a transition between a contracting and an expanding universe in the Einstein frame. Following up on previous work that uncovered such bouncing solutions in the context of weakly coupled thermal configurations of a certain class of type II superstrings, we set up here the formalism in which we can study the evolution of metric fluctuations across such an S-brane. Our work shows that the specific nature of the S-brane, which is sourced by non-trivial massless thermal string states and appears when the universe reaches a maximal critical temperature, allows for a scale invariant spectrum of curvature fluctuations to manifest at late times via a stringy realization of the matter bounce scenario. The finite energy density at the transition from contraction to expansion provides calculational control over the propagation of the curvature perturbations through the bounce, furnishing a working proof of concept that such a stringy universe can result in viable late time cosmology.

hep-th↗

arXiv2013

Correlating features in the primordial spectra

Heavy fields coupled to the inflaton reduce the speed of sound in the effective theory of the adiabatic mode each time the background inflationary trajectory deviates from a geodesic. This can result in features in the primordial spectra. We compute the corresponding bispectrum and show that if a varying speed of sound induces features in the power spectrum, the change in the bispectrum is given by a simple formula involving the change in the power spectrum and its derivatives. In this manner, we provide a uniquely discriminable signature of a varying sound speed for the adiabatic mode during inflation that indicates the influence of heavy fields. We find that features in the bispectrum peak in the equilateral limit and, in particular, in the squeezed limit we find considerable enhancement entirely consistent with the single field consistency relation. From the perspective of the underlying effective theory, our results generalize to a wide variety of inflationary models where features are sourced by the time variation of background quantities. A positive detection of such correlated features would be unambiguous proof of the inflaton's nature as a single light scalar degree of freedom embedded in a theory that is UV completable.

astro-ph.CO↗

arXiv2013

Inflating in a Trough: Single-Field Effective Theory from Multiple-Field Curved Valleys

We examine the motion of light fields near the bottom of a potential valley in a multi-dimensional field space. In the case of two fields we identify three general scales, all of which must be large in order to justify an effective low-energy approximation involving only the light field, $\ell$. (Typically only one of these -- the mass of the heavy field transverse to the trough -- is used in the literature when justifying the truncation of heavy fields.) We explicitly compute the resulting effective field theory, which has the form of a $P(\ell,X)$ model, with $X = - 1/2(\partial \ell)^2$, as a function of these scales. This gives the leading ways each scale contributes to any low-energy dynamics, including (but not restricted to) those relevant for cosmology. We check our results with the special case of a homogeneous roll near the valley floor, placing into a broader context recent cosmological calculations that show how the truncation approximation can fail. By casting our results covariantly in field space, we provide a geometrical criterion for model-builders to decide whether or not the single-field and/or the truncation approximation is justified, identify its leading deviations, and to efficiently extract cosmological predictions.

hep-th↗

arXiv2012

Heavy fields, reduced speeds of sound and decoupling during inflation

We discuss and clarify the validity of effective single field theories of inflation obtained by integrating out heavy degrees of freedom in the regime where adiabatic perturbations propagate with a suppressed speed of sound. We show by construction that it is indeed possible to have inflationary backgrounds where the speed of sound remains suppressed and slow-roll persists for long enough. In this class of models, heavy fields influence the evolution of adiabatic modes in a manner that is consistent with decoupling of physical low and high energy degrees of freedom. We emphasize the distinction between the effective masses of the isocurvature modes and the eigenfrequencies of the propagating high energy modes. Crucially, we find that the mass gap that defines the high frequency modes increases with the strength of the turn, even as the naive heavy (isocurvature) and light (curvature) modes become more strongly coupled. Adiabaticity is preserved throughout, and the derived effective field theory remains in the weakly coupled regime, satisfying all current observational constraints on the resulting primordial power spectrum. In addition, these models allow for an observably large equilateral non-Gaussianity.

hep-th↗

arXiv2012

Effective theories of single field inflation when heavy fields matter

We compute the low energy effective field theory (EFT) expansion for single-field inflationary models that descend from a parent theory containing multiple other scalar fields. By assuming that all other degrees of freedom in the parent theory are sufficiently massive relative to the inflaton, it is possible to derive an EFT valid to arbitrary order in perturbations, provided certain generalized adiabaticity conditions are respected. These conditions permit a consistent low energy EFT description even when the inflaton deviates off its adiabatic minimum along its slowly rolling trajectory. By generalizing the formalism that identifies the adiabatic mode with the Goldstone boson of this spontaneously broken time translational symmetry prior to the integration of the heavy fields, we show that this invariance of the parent theory dictates the entire non-perturbative structure of the descendent EFT. The couplings of this theory can be written entirely in terms of the reduced speed of sound of adiabatic perturbations. The resulting operator expansion is distinguishable from that of other scenarios, such as standard single inflation or DBI inflation. In particular, we re-derive how certain operators can become transiently strongly coupled along the inflaton trajectory, consistent with slow-roll and the validity of the EFT expansion, imprinting features in the primordial power spectrum, and we deduce the relevant cubic operators that imply distinct signatures in the primordial bispectrum which may soon be constrained by observations.

hep-th↗

arXiv2011

Features of heavy physics in the CMB power spectrum

The computation of the primordial power spectrum in multi-field inflation models requires us to correctly account for all relevant interactions between adiabatic and non-adiabatic modes around and after horizon crossing. One specific complication arises from derivative interactions induced by the curvilinear trajectory of the inflaton in a multi-dimensional field space. In this work we compute the power spectrum in general multi-field models and show that certain inflaton trajectories may lead to observationally significant imprints of `heavy' physics in the primordial power spectrum if the inflaton trajectory turns, that is, traverses a bend, sufficiently fast (without interrupting slow roll), even in cases where the normal modes have masses approaching the cutoff of our theory. We emphasise that turning is defined with respect to the geodesics of the sigma model metric, irrespective of whether this is canonical or non-trivial. The imprints generically take the form of damped superimposed oscillations on the power spectrum. In the particular case of two-field models, if one of the fields is sufficiently massive compared to the scale of inflation, we are able to compute an effective low energy theory for the adiabatic mode encapsulating certain relevant operators of the full multi-field dynamics. As expected, a particular characteristic of this effective theory is a modified speed of sound for the adiabatic mode which is a functional of the background inflaton trajectory and the turns traversed during inflation. Hence in addition, we expect non-Gaussian signatures directly related to the features imprinted in the power spectrum.

hep-ph↗