arXiv subjects

Tomislav Prokopec

Publications and source records attributed to Tomislav Prokopec.

At least 37 records · Page 2Linked to original sources

arXiv2022

Spatial correlations of dark energy from quantum fluctuations in inflation

This paper contains a detailed study of the properties of a simple model attempting to explain dark energy as originated from quantum fluctuations of a light spectator scalar field in inflation. In [1] we recently outlined how Starobinsky's stochastic formalism can be used to study the spatial correlations imprinted on dark energy by its quantum origin in this model and we studied their possible role in relieving the Hubble tension. Here we provide a more comprehensive derivation of the results in [1] and we refine some of our estimates, comparing to the approximate results obtained previously. Among the main results, we analyze the non-coincident correlators predicted by a full field theoretical treatment and their relation with those computed within the stochastic formalism. We find that in the region where stochastic theory predicts significant sub-Hubble correlators it is in disagreement with field theoretical predictions. However, agreement can be restored by introducing a reduced speed of sound for the scalar field. We also discuss an alternative approach to the problem of studying correlators within the stochastic formalism based directly on the evolution of probability distributions. We find that the two approaches give the same answer for 2-point functions of the field, but not for 4-point functions relevant to density correlators and we discuss the behaviour of the two methods with respect to Wick's theorem.

gr-qc↗

arXiv2022

Quantum origin of dark energy and the Hubble tension

Local measurements of the Hubble parameter obtained from the distance ladder at low redshift are in tension with global values inferred from cosmological standard rulers. A key role in the tension is played by the assumptions on the cosmological history, in particular on the origin of dark energy. Here we consider a scenario where dark energy originates from the amplification of quantum fluctuations of a light field in inflation. We show that spatial correlations inherited from inflationary quantum fluctuations can reduce the Hubble tension down to one standard deviation, thus relieving the problem with respect to the standard cosmological model. Upcoming missions, like Euclid, will be able to test the predictions of models in this class.

astro-ph.CO↗

arXiv2022

Scalar propagator for planar gravitational waves

We construct the massive scalar propagator for planar gravitational wave backgrounds propagating on Minkowski space. We represent the propagator in terms of the Bessel's function of suitably deformed nonlocal distance functions, the deformation being caused by gravitational waves. We calculate the propagator both for nonpolarized, for the plus ($+$) and cross ($\times$) polarized plane waves, as well as for more general planar waves both in $D$ space-time dimensions. The propagator is useful for studying interactions of scalar fields on planar gravitational wave backgrounds in the context of interacting quantum fields, in which renormalization plays a crucial role. As simple applications of the propagator we calculate the one-loop effective action, the scalar mass generated by the scalar self-interaction term and the one-loop energy-momentum tensor, all renormalized by using dimensional regularization and renormalization. While the effective action and scalar mass remain unaffected by gravitational waves, the energy-momentum tensor exhibits flow of energy density in the direction of gravitational waves which grows quadratically with the scalar field mass, gravitational wave amplitude and its frequency.

gr-qc↗

arXiv2022

Majorana propagator on de Sitter space

We study the dynamics of Majorana fermions in an expanding de Sitter space and to that aim we construct the vacuum Feynman propagator for Majorana fermions in de Sitter space. Surprisingly, the Majorana propagator is identical to that of the Dirac fermions. We then use this propagator and calculate the one-loop effective action for Majorana fermions, and show that it differs from that of Dirac fermions by a factor of 1/2, which accounts for the reduced number of degrees of freedom of the Majorana particle. Finally, we derive the Majorana and Dirac propagators for mixing fermionic flavors, which are suitable for studying CP-violating effects in quantum loops.

hep-th↗

arXiv2021

$Δ\mathcal{N}$ and the stochastic conveyor belt of Ultra Slow-Roll

We analyse field fluctuations during an Ultra Slow-Roll phase in the stochastic picture of inflation and the resulting non-Gaussian curvature perturbation, fully including the gravitational backreaction of the field's velocity. By working to leading order in a gradient expansion, we first demonstrate that consistency with the momentum constraint of General Relativity prevents the field velocity from having a stochastic source, reflecting the existence of a single scalar dynamical degree of freedom on long wavelengths. We then focus on a completely level potential surface, $V=V_0$, extending from a specified exit point $ϕ_{\rm e}$, where slow roll resumes or inflation ends, to $ϕ\rightarrow +\infty$. We compute the probability distribution in the number of e-folds $\mathcal{N}$ required to reach $ϕ_{\rm e}$ which allows for the computation of the curvature perturbation. We find that, if the field's initial velocity is high enough, all points eventually exit through $ϕ_{\rm e}$ and a finite curvature perturbation is generated. On the contrary, if the initial velocity is low, some points enter an eternally inflating regime despite the existence of $ϕ_{\rm e}$. In that case the probability distribution for $\mathcal{N}$, although normalizable, does not possess finite moments, leading to a divergent curvature perturbation.

gr-qc↗

arXiv2021

Abelian Higgs model in power-law inflation: the propagators in the unitary gauge

We consider the Abelian Higgs model in the broken phase as a spectator in cosmological spaces of general $D$ space-time dimensions, and allow for the condensate to be time-dependent. We fix the unitary gauge using Dirac's formalism for constrained systems, and then quantize the gauge-fixed system. Vector and scalar perturbations develop time-dependent masses. We work out their propagators assuming the cosmological background is that of power-law inflation, characterized by a constant principal slow-roll parameter, and that the scalar condensate is in the attractor regime, scaling as the Hubble rate. Our propagators correctly reduce to known results in the Minkowski and de Sitter space limits. We use the vector propagator to compute the equal-time correlators of electric and magnetic fields and find that at super-Hubble separations the former is enhanced, while the latter is suppressed compared to the vacuum fluctuations of the massless vector field. These correlators satisfy the hierarchy governed by Faraday's law.

gr-qc↗

arXiv2021

Non-minimally coupled curvaton

We investigate two-field inflationary models in which scalar cosmological pertubations are generated via a spectator field nonminimally coupled to gravity, with the particular emphasis on curvaton scenarios. The principal advantage of these models is in the possibility to tune the spectator spectral index via the nonminimal coupling. Our models naturally yield red spectrum of the adiabatic perturbation demanded by observations. We study how the nonminimal coupling affects the spectrum of the curvature perturbation generated in the curvaton scenarios. In particular we find that for small, negative nonminimal couplings the spectral index gets a contribution that is negative and linear in the nonminimal coupling. Since in this way the curvature spectrum becomes redder, some of curvaton scenarios can be saved, which would otherwise be ruled out. In the power law inflation we find that a large nonminimal coupling is excluded since it gives the principal slow roll parameter that is of the order of unity. Finally, we point out that nonminimal coupling can affect the postinflationary growth of the spectator perturbation, and in this way the effectiveness of the curvaton mechanism.

astro-ph.CO↗

arXiv2021

Field-theoretic derivation of bubble-wall force

We derive a general quantum field theoretic formula for the force acting on expanding bubbles of a first order phase transition in the early Universe setting. In the thermodynamic limit the force is proportional to the entropy increase across the bubble of active species that exert a force on the bubble interface. When local thermal equilibrium is attained, we find a strong friction force which grows as the Lorentz factor squared, such that the bubbles quickly reach stationary state and cannot run away. We also study an opposite case when scatterings are negligible across the wall (ballistic limit), finding that the force saturates for moderate Lorentz factors thus allowing for a runaway behavior. We apply our formalism to a massive real scalar field, the standard model and its simple portal extension. For completeness, we also present a derivation of the renormalized, one-loop, thermal energy-momentum tensor for the standard model and demonstrate its gauge independence.

hep-th↗

arXiv2019

Field-theoretic approach to large-scale structure formation

We develop a field-theoretic description of large-scale structure formation by taking the non-relativistic limit of a canonically transformed, real scalar field which is minimally coupled to scalar gravitational perturbations in longitudinal gauge. We integrate out the gravitational constraint fields and arrive at a non-local action which is only specified in terms of the dynamical degrees of freedom. In order to make this framework closer to the classical particle description, we construct the corresponding 2PI effective action truncated at two loop order for a non-squeezed state without field expectation values. We contrast the dynamical description of the coincident time phase-space density to the standard Vlasov description of cold dark matter particles and identify momentum and time scales at which linear perturbation theory will deviate from the standard evolution.

gr-qc↗

arXiv2019

Entropy production in inflation from spectator loops

Perturbations in cosmic microwave background (CMB) photons and large scale structure of the universe are sourced primarily by the curvature perturbation which is widely believed to be produced during inflation. In this paper we present a 2-field inflationary model in which the inflaton couples bi-quadratically to a spectator field. We show that the spectator induces a rapid growth of the momentum of the curvature perturbation and the associated Gaussian van Neumann entropy during inflation such that the initial conditions at the end of inflation are substantially different from the standard ones. Consequently, one ought to reconsider the kinetic equations describing evolution of the photon, dark matter and baryonic fluids in radiation and matter eras and take account of the fact that the curvature perturbation and its canonical momentum are two {\it a priory} independent stochastic fields. We also briefly analyze possible imprints on the CMB temperature fluctuations from the more general inflationary scenario which contains light spectator fields coupled to the inflaton.

astro-ph.CO↗

arXiv2019

Failure of the stochastic approach to inflation beyond slow-roll

After giving a pedagogical review we clarify that the stochastic approach to inflation is generically reliable only at zeroth order in the (geometrical) slow-roll parameter $ε_1$ if and only if $ε_2^2\ll 6/ε_1$, with the notable exception of slow-roll. This is due to the failure of the stochastic $ΔN$ formalism in its standard formulation. However, by keeping the formalism in its regime of validity, we showed that, in ultra-slow-roll, the stochastic approach to inflation reproduces the power spectrum calculated from the linear theory approach.

gr-qc↗

arXiv2019

Gravitational waves from conformal symmetry breaking

We consider the electroweak phase transition in the conformal extension of the standard model known as SU(2)cSM. Apart from the standard model particles, this model contains an additional scalar and gauge field that are both charged under the hidden SU(2)$_X$. This model generically exhibits a very strong phase transition that proceeds after a large amount of supercooling. We estimate the gravitational wave spectrum produced in this model and show that its amplitude and frequency fall within the observational window of LISA. We also discuss potential pitfalls and relevant points of improvement required to attain reliable estimates of the gravitational wave production in this - as well as in more general - class of models. In order to improve perturbativity during the early stages of transition that ends with bubble nucleation, we solve a thermal gap equation in the scalar sector inspired by the 2PI effective action formalism.

hep-ph↗

arXiv2018

Conformal symmetry and the cosmological constant problem

We argue that, when a theory of gravity and matter is endowed with (classical) conformal symmetry, the fine tuning required to obtain the cosmological constant at its observed value can be significantly reduced. Once tuned, the cosmological constant is stable under a change of the scale at which it is measured.

gr-qc↗

arXiv2018

Phase Space Non-commutativity and its Stability

We consider a generalised non-commutative space-time in which non-commutativity is extended to all phase space variables. If strong enough, non-commutativity can affect stability of the system. We perform stability analysis on a couple of simple examples and show that a system can be stabilised by introducing quartic interactions provided they satisfy phase-space copositivity. In order to conduct perturbative analysis of these systems one can use either canonical methods or phase-space path integral methods which we present in some detail.

hep-th↗

arXiv2018

Systematic analysis of radiative symmetry breaking in models with extended scalar sector

Radiative symmetry breaking (RSB) is a theoretically appealing framework for the generation of mass scales through quantum effects. It can be successfully implemented in models with extended scalar and gauge sectors. We provide a systematic analysis of RSB in such models: we review the common approximative methods of studying RSB, emphasising their limits of applicability and discuss the relevance of the relative magnitudes of tree-level and loop contributions as well as the dependence of the results on the renormalisation scale. The general considerations are exemplified within the context of the conformal Standard Model extended with a scalar doublet of a new SU(2)$_X$ gauge group, the so-called SU(2)cSM. We show that various perturbative methods of studying RSB may yield significantly different results due to renormalisation-scale dependence. Implementing the renormalisation-group (RG) improvement method recently developed in arXiv:1801.05258, which is well-suited for multi-scale models, we argue that the use of the RG improved effective potential can alleviate this scale dependence providing more reliable results.

hep-ph↗

arXiv2018

Functional renormalization group in stochastic inflation

We apply the functional renormalization group to Starobinsky's stochastic equation describing the local dynamics of a light scalar field in de Sitter. After elaborating on the over-damped regime of stochastic dynamics, we introduce an effective average action for the stochastic field, resulting by progressively integrating out frequencies, and study its flow equation in the local potential approximation (LPA). This effective action determines the approach to equilibrium and allows for the computation of unequal time correlators $\left\langleϕ(t)ϕ(t+Δt)\right\rangle$ for large values of $Δt$. The stochastic RG flow in the LPA can be formulated in two ways, one that preserves the stochastic supersymmetry and one that breaks it. We show that both predict a characteristic decay time very close to that determined by the dynamical mass for a massless self-interacting scalar in de Sitter $m^2\sim \sqrtλH^2$. Furthermore, the temporal supersymmetric formulation remarkably recovers the flow for the effective potential found using Quantum Field Theory methods and a smoothing over spatial wavelengths. We also discuss how the stochastic framework generically predicts an infrared mass which is a few percent smaller than the dynamical mass obtained in the LPA. Our results further support the notion that stochastic inflation captures the correct IR dynamics of light scalar fields in inflation.

gr-qc↗

arXiv2018

Kinetic theory and classical limit for real scalar quantum field in curved space-time

Starting from a real scalar quantum field theory with quartic self-interactions and non-minimal coupling to classical gravity, we define four equal-time, spatially covariant phase-space operators through a Wigner transformation of spatially translated canonical operators within a 3+1 decomposition. A subset of these operators can be interpreted as fluctuating particle densities in phase-space whenever the quantum state of the system allows for a classical limit. We come to this conclusion by expressing hydrodynamic variables through the expectation values of these operators and moreover, by deriving the dynamics of the expectation values within a spatial gradient expansion and a 1-loop approximation which subsequently yields the Vlasov equation with a self-mass correction as a limit. We keep an arbitrary classical metric in the 3+1 decomposition which is assumed to be determined semi-classically. Our formalism allows to systematically study the transition from quantum field theory in curved space-time to classical particle physics for this minimal model of self-interacting, gravitating matter. As an application we show how to include relativistic and self-interaction corrections to existing dark matter models in a kinetic description by taking into account the gravitational slip, vector perturbations and tensor perturbations.

gr-qc↗

arXiv2018

Inflation in an effective gravitational model & asymptotic safety

We consider an inflationary model motivated by quantum effects of gravitational and matter fields near the Planck scale. Our Lagrangian is a re-summed version of the effective Lagrangian recently obtained by Demmel, Saueressig and Zanusso~\cite{Demmel:2015oqa} in the context of gravity as an asymptotically safe theory. It represents a refined Starobinsky model, ${\cal L}_{\rm eff}=M_{\rm P}^2 R/2 + (a/2)R^2/[1+b\ln(R/μ^2)]$, where $R$ is the Ricci scalar, $a$ and $b$ are constants and $μ$ is an energy scale. By implementing the COBE normalisation and the Planck constraint on the scalar spectrum, we show that increasing $b$ leads to an increased value of both the scalar spectral index $n_s$ and the tensor-to-scalar ratio $r$. Requiring $n_s$ to be consistent with the Planck collaboration upper limit, we find that $r$ can be as large as $r\simeq 0.01$, the value possibly measurable by Stage IV CMB ground experiments and certainly from future dedicated space missions. The predicted running of the scalar spectral index $α=d n_s/d\ln(k)$ is still of the order $-5\times 10^{-4}$ (as in the Starobinsky model), about one order of magnitude smaller than the current observational bound.

gr-qc↗