Papers by Tomislav Prokopec
The European Physical Journal C
We study the dynamics of Majorana fermions in an expanding de Sitter space and to that aim, by ma... more We study the dynamics of Majorana fermions in an expanding de Sitter space and to that aim, by making use of the method of mode sums, we construct the vacuum Feynman propagator for Majorana fermions in de Sitter space. The Majorana condition implies nontrivial identities for the mode functions, which we carefully implement. We note that, under charge conjugation, the propagator transforms to minus itself, but do not discuss in detail the topological implications of this observation. We construct the propagator for a general complex mass and find that it is identical to the corresponding Dirac propagator, meaning that the coupling of fermions to the classical de Sitter gravitational background does not violate charge symmetry, i.e. it respects the Majorana condition. The complex mass propagator differs from its real mass counterpart in that the usual positive and negative energy projectors acquire a chiral rotation which depends on the phase of the mass term. We use our propagator to...
arXiv (Cornell University), Sep 1, 2022
The origin of dark energy driving the accelerated expansion of the universe is still mysterious. ... more The origin of dark energy driving the accelerated expansion of the universe is still mysterious. We explore the possibility that dark energy fluctuates, resulting in spatial correlations. Due to these fluctuations, the Hubble rate itself becomes a fluctuating quantity. We discuss the effect this has on measurements of type Ia supernovae, which are used to constrain the luminosity distance. We show that the luminosity distance is affected by spatial correlations in several ways. First, the luminosity distance becomes dressed by the fluctuations, thereby differing from standard ΛCDM. Second, angular correlations become visible in the two-point correlation function of the luminosity distance. To investigate the latter we construct the angular power spectrum of luminosity distance fluctuations. We then perform a forecast for two supernova surveys, the ongoing Dark Energy Survey (DES) and the upcoming Legacy Survey of Space and Time (LSST), and compare this effect with relativistic lensing effects from perturbed ΛCDM. We find that the signal can rise above the lensing effects and that LSST could test this effect for a large part of the parameter space. As an example, a specific realisation of such a scenario is that quantum fluctuations of some field in the early universe imprint spatial correlations with a predictable form in the dark energy density today. In this case, the Hubble rate fluctuates due to the intrinsic quantum nature of the dark energy density field. We study whether the signal of this specific model would be measurable, and conclude that testing this model with LSST would be challenging. However, taking into account a speed of sound c s < 1 of the dark energy fluid can make this model observable.
Journal of Cosmology and Astroparticle Physics
The origin of dark energy driving the accelerated expansion of the universe is still mysterious. ... more The origin of dark energy driving the accelerated expansion of the universe is still mysterious. We explore the possibility that dark energy fluctuates, resulting in spatial correlations. Due to these fluctuations, the Hubble rate itself becomes a fluctuating quantity. We discuss the effect this has on measurements of type Ia supernovae, which are used to constrain the luminosity distance. We show that the luminosity distance is affected by spatial correlations in several ways. First, the luminosity distance becomes dressed by the fluctuations, thereby differing from standard ΛCDM. Second, angular correlations become visible in the two-point correlation function of the luminosity distance. To investigate the latter we construct the angular power spectrum of luminosity distance fluctuations. We then perform a forecast for two supernova surveys, the ongoing Dark Energy Survey (DES) and the upcoming Legacy Survey of Space and Time (LSST), and compare this effect with relativistic lensi...
arXiv (Cornell University), Jun 25, 2018
We consider a generalised non-commutative space-time in which non-commutativity is extended to al... more 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.
Journal of High Energy Physics, 2021
We derive a general quantum field theoretic formula for the force acting on expanding bubbles of ... more 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.
Physical Review D, 2017
We develop a hybrid formalism suitable for modeling scalar field dark matter, in which the phase-... more We develop a hybrid formalism suitable for modeling scalar field dark matter, in which the phase-space distribution associated to the real scalar field is modeled by statistical equaltime two-point functions and gravity is treated by two stochastic gravitational fields in the longitudinal gauge (in this work we neglect vector and tensor gravitational perturbations). Inspired by the commonly used Newtonian Vlasov-Poisson system, we firstly identify a suitable combination of equal-time two-point functions that defines the phase-space distribution associated to the scalar field and then derive both a kinetic equation that contains relativistic scalar matter corrections as well as linear gravitational scalar field equations whose sources can be expressed in terms of a momentum integral over the phase-space distribution function. Our treatment generalizes the commonly used classical scalar field formalism, in that it allows for modeling of (dynamically generated) vorticity and perturbations in anisotropic stresses of the scalar field. It also allows for a systematic inclusion of relativistic and higher order corrections that may be used to distinguish different dark matter scenarios. We also provide initial conditions for the statistical equal-time two-point functions of the matter scalar field in terms of gravitational potentials and the scale factor.
Physics of the Dark Universe, 2017
Recently, it has been claimed that inflationary models with an inflection point in the scalar pot... more Recently, it has been claimed that inflationary models with an inflection point in the scalar potential can produce a large resonance in the power spectrum of curvature perturbation. In this paper however we show that the previous analyses are incorrect. The reason is twofold: firstly, the inflaton is overshot from a stage of standard inflation and so deviates from the slow-roll attractor before reaching the inflection. Secondly, on the (or close to) the inflection point, the ultra-slow-roll trajectory supersede the slow-roll one and thus, the slow-roll approximations used in the literature cannot be used. We then reconsider the model and provide a recipe for how to produce nevertheless a large peak in the matter power spectrum via fine-tuning of parameters.
Cornell University - arXiv, Nov 30, 2022
The large scale geometry of the late Universe can be decomposed as R × Σ 3 , where R stands for c... more The large scale geometry of the late Universe can be decomposed as R × Σ 3 , where R stands for cosmic time and Σ 3 is the three dimensional spatial manifold. We conjecture that the spatial geometry of the Universe's spatial section Σ 3 conforms with the Thurston-Perelman theorem, according to which the geometry of Σ 3 is either one of the eight geometries from the Thurston geometrization conjecture, or a combination of Thurston geometries smoothly sewn together. We assume that topology of individual geometries plays no observational role, i.e. the size of individual geometries is much larger than the Hubble radius today. We investigate the dynamics of each of the individual geometries by making use of the simplifying assumption that our local Hubble patch consists of only one such geometry, which is approximately homogeneous on very large scales, but spatial isotropy is generally violated. Spatial anisotropies grow in time in decelerating universes, but they decay in accelerating universes. The thuscreated anisotropy problem can be solved by a period of primordial inflation, akin to how the flatness problem is solved. Therefore, as regards Universe's large scale geometry, any of the Thurston's geometries should be considered on a par with Friedmann's geometries. We consider two observational methods that can be used to test our conjecture: one based on luminosity distance and one on angular diameter distance measurements, but leave for the future their detailed forecasting implementations.
Cornell University - arXiv, Sep 1, 2017
The conformal anomaly (also known as the stress-energy trace anomaly) of an interacting quantum t... more The conformal anomaly (also known as the stress-energy trace anomaly) of an interacting quantum theory, associated with violation of Weyl (conformal) symmetry by quantum effects, can be amended if one endows the theory with a dilatation current coupled to a vector field that is the gauge connection of local Weyl symmetry transformations. The natural candidate for this Weyl connection is the trace of the geometric torsion tensor, especially if one recalls that pure (Cartan-Einstein) gravity with torsion is conformal. We first point out that both canonical and path integral quantisation respect Weyl symmetry. The only way quantum effects can violate conformal symmetry is by the process of regularization. However, if one calculates an effective action from a conformally invariant classical theory by using a regularisation procedure that is conform with Weyl symmetry, then the conformal Ward identities will be satisfied. In this sense Weyl symmetry is not broken by quantum effects. This work suggests that Weyl symmetry can be treated on equal footing with gauge symmetries and gravity, for which an infinite set of Ward identities guarantees that they remain unbroken by quantum effects.
Physical Review D, 2016
We investigate the backreaction of the quantum fluctuations of a very light (m H today) nonminima... more We investigate the backreaction of the quantum fluctuations of a very light (m H today) nonminimally coupled spectator scalar field on the expansion dynamics of the Universe. The one-loop expectation value of the energy momentum tensor of these fluctuations, as a measure of the backreaction, is computed throughout the expansion history from the early inflationary universe until the onset of recent acceleration today. We show that, when the nonminimal coupling ξ to Ricci curvature is negative (ξ c = 1/6 corresponding to conformal coupling), the quantum backreaction grows exponentially during inflation, such that it can grow large enough rather quickly (within a few hundred e-foldings) to survive until late time and constitute a contribution of the cosmological constant type of the right magnitude to appreciably alter the expansion dynamics. The unique feature of this model is in that, under rather generic assumptions, inflation provides natural explanation for the initial conditions needed to explain the late-time accelerated expansion of the Universe, making it a particularly attractive model of dark energy.
Journal of Cosmology and Astroparticle Physics, 2009
We generalize the effective potential to scalar field configurations which are proportional to th... more We generalize the effective potential to scalar field configurations which are proportional to the Hubble parameter of a homogeneous and isotropic background geometry. This may be useful in situations for which curvature effects are significant. We evaluate the one loop contribution to the Hubble Effective Potential for a massless scalar with arbitrary conformal and quartic couplings, on a background for which the deceleration parameter is constant. Among other things, we find that inflationary particle production leads to symmetry restoration at late times.
Classical and Quantum Gravity, 2016
In this paper we consider conformal symmetry in the context of manifolds with general affine conn... more In this paper we consider conformal symmetry in the context of manifolds with general affine connection. We extend the conformal transformation law of the metric to a general metric compatible affine connection, and find that it is a symmetry of both the geodesic equation and the Riemann tensor. We derive the generalised Jacobi equation and Raychaudhuri equation and show that they are both conformally invariant. Using the geodesic deviation (Jacobi) equation we analyse the behaviour of geodesics in different conformal frames. Since we find that our version of conformal symmetry is exact in classical pure Einstein's gravity, we ask whether one can extend it to the standard model. We find that it is possible to write conformal invariant lagrangians in any dimensions for vector, fermion and scalar fields, but that such lagrangians are only gauge invariant in four dimensions. Provided one introduces a dilaton field, gravity can be conformally coupled to matter.
We investigate whether quantum fluctuations can have a significant impact on the evolution of the... more We investigate whether quantum fluctuations can have a significant impact on the evolution of the universe, by studying the (late-time) backreaction of a massless scalar field with a possible coupling ξ to the Ricci scalar on an FLRW background. The main motivation for this work is the observed late-time acceleration of the universe, for which no satisfactory explanation has been given yet. At the same time, cosmological perturbation theory establishes that we can take quantum fluctuations in a gravitational setting seriously, and some of their effects are well studied and in agreement with observations. This opens up the question if the energy density and pressure of these quantum fluctuations could account for the observed late-time acceleration of the universe. In addition to the usually assumed history of the universe (an inflationary, radiation and matter dominated period), we assume an initial radiation period in order to resolve IR divergences that are otherwise present in tw...
Physical Review D, 2018
Starting from a real scalar quantum field theory with quartic self-interactions and nonminimal co... more Starting from a real scalar quantum field theory with quartic self-interactions and nonminimal 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 þ 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 one-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 þ 1 decomposition which is assumed to be determined semiclassically. Our formalism allows us to systematically study the transition from quantum field theory in curved spacetime 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.
Journal of Cosmology and Astroparticle Physics, 2019
In this paper we study a novel realization of inflation, based on Weyl invariant gravity with tor... more In this paper we study a novel realization of inflation, based on Weyl invariant gravity with torsion. We show that requiring the classical action for the scalar field to be Weyl invariant introduces a dilaton which induces a non trivial modification of the field space geometry of the scalar sector, which allows for inflationary phase that begins at the conformal point of the inflaton ψ, i.e. ψ = 0. Since the model is Weyl invariant, the inflaton condensation models a process of spontaneous Weyl symmetry breaking. For a wide range of parameters the spectral observables of the model are in good agreement with the CMB measurements, such that the scalar spectral index and the tensor-to-scalar ratio approximately agree with those of Starobinsky's inflation, i.e. n s 0.96 − 0.97 and r ≈ 3 × 10 −3. The simplest version of our model contains two scalar degrees of freedom, one of them being an exactly flat direction. If that degree is excited early on in inflation and if inflation lasts for about 60 e-foldings, we find that the Unverse undergoes a short period of kination that predates inflation. Such a period strongly suppresses the amplitude of large scale CMB temperature fluctuations providing thus an elegant explanation for the lack of power in the lowest CMB multipoles.
Classical and Quantum Gravity, 2014
We calculate the one-loop corrections from inflationary gravitons to the electromagnetic fields o... more We calculate the one-loop corrections from inflationary gravitons to the electromagnetic fields of a point charge and a point magnetic dipole on a locally de Sitter space background. Results are obtained both for an observer at rest in co-moving coordinates, whose physical distance from the sources increases with the expanding universe, and for an observer at rest in static coordinates, whose physical distance from the sources is constant. The fields of both sources show the de Sitter analogs of the fractional G/r 2 corrections which occur in flat space, but there are also some fractional GH 2 corrections due to the scattering of virtual photons from the vast ensemble of infrared gravitons produced by inflation. The co-moving observer perceives the magnitude of the point charge to increase linearly with co-moving time and logarithmically with the co-moving position, however, the magnetic dipole shows only a negative logarithmic spatial variation. The static observer perceives no secular change of the point charge but he does report a secular enhancement of the magnetic dipole moment.
Physical Review D, 2002
We derive a semiclassical transport equation for fermions propagating in the presence of a CP-vio... more We derive a semiclassical transport equation for fermions propagating in the presence of a CP-violating planar bubble wall at a first order electroweak phase transition. Starting from the Kadanoff-Baym (KB) equation for the two-point (Wightman) function we perform an expansion in gradients, or equivalently in the Planck constanth. We show that to first order inh the KB equations have a spectral solution, which allows for an on-shell description of the plasma excitations. The CP-violating force acting on these excitations is found to be enhanced by a boost factor in comparison with the 1+1-dimensional case studied in a former paper. We find that an identical semiclassical force can be obtained by the WKB method. Applications to the MSSM are also mentioned.
Annals of Physics, 2010
We consider the quantum Friedmann equations which include one-loop vacuum fluctuations due to gra... more We consider the quantum Friedmann equations which include one-loop vacuum fluctuations due to gravitons and scalar field matter in a FLRW background with constant ǫ = −Ḣ/H 2. After several field redefinitions, to remove the mixing between the gravitational and matter degrees of freedom, we can construct the one loop correction to the Friedmann equations. Due to cosmological particle creation, the propagators needed in such a calculation are typically infrared divergent. In this paper we construct the graviton and matter propagators, making use of the recent construction of the infrared finite scalar propagators calculated on a compact spatial manifold in [1]. The resulting correction to the Friedman equations is suppressed with respect to the tree level contribution by a factor of H 2 /m 2 p and shows no secular growth.
Physical Review D, 2015
We consider the late time one-loop quantum backreaction from inflationary fluctuations of a non-m... more We consider the late time one-loop quantum backreaction from inflationary fluctuations of a non-minimally coupled, massless scalar field. The scalar is assumed to be a spectator field in an inflationary model with a constant principal slow roll parameter. We regulate the infrared by matching onto a pre-inflationary radiation era. We find a large late time backreaction when the nonminimal coupling ξ is negative (in which case the scalar exhibits a negative mass term during inflation). The one-loop quantum backreaction becomes significant today for moderately small nonminimal couplings, ξ ∼ −1/20, and it changes sign (from negative to positive) at a recent epoch when inflation lasts not much longer than what is minimally required, N 66. Since currently we do not have a way of treating the classical fluid and the quantum backreaction in a self-consistent manner, we cannot say decidely whether the backreaction from inflationary quantum fluctuations of a non-minimally coupled scalar can mimic dark energy.
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Papers by Tomislav Prokopec