Abstract We investigate gauge dependence of one-graviton-loop corrections to the effective field equation of the massless, minimally coupled scalar in de Sitter, obtained by including source and observer corrections to the effective self-mass correcting the equation. Using the ∆α variation of the de Sitter-breaking graviton propagator in a one-parameter family of gauges, we compute the gauge-dependent contributions to the effective self-mass of a massless minimally coupled scalar mediating interactions between heavy scalars. We show that gauge dependence cancels provided the contributions from all diagram classes are collected, including one-loop corrections to external mode functions, which play a qualitatively new role relative to flat space. The resulting cancellation supports the construction of graviton gauge-independent cosmological quantum-gravitational observables from quantum-corrected effective equations.

We investigate the quantum stability of a timelike topological wormhole with a simple geometry M_2 × S^2, supported classically by anisotropic fluid. We compute the one-loop quantum backreaction generated by the vacuum fluctuations of a minimally coupled, massive scalar field propagating on the wormhole background. Using dimensional regularization we renormalize the one-loop energy-momentum tensor and identify the necessary gravitational counterterms. We then solve the semiclassical Einstein equations to linear order in ħ for both time-dependent and static metric Ansätze. Depending on the choice of finite counterterms, the quantum effects can induce either negative or positive angular pressure, which will tend to destabilize or stablize the wormhole, respectively. We also show that a classically traversable wormhole will remain traversable when the quantum backreaction is taken into account. It would be of interest to investigate whether these conclusions remain true when the equations of semiclassical gravity are self-consistently solved.

The growth of primordial perturbations during the matter-dominated era is primarily driven by dark matter. Ultralight scalar fields (ULDM) are a promising candidate for this role, conventionally modeled as operating in a classical, high-occupation regime. In this work, we develop a first-principles field-theoretic framework to investigate the impact of ULDM on linear cosmological perturbations during matter domination, explicitly retaining its quantum nature. Deriving a closed equation for the graviton field dynamics, we compute and regularize its source terms for a generic Gaussian initial state of the ULDM field within the adiabatic (WKB) approximation, employing the middle-point working assumption for non-local terms. After gauge-fixing we find that, contrary to previous claims, the classical condensate of ULDM has no influence on gravitational wave propagation. However, the time-dependent graviton effective mass induced by quantum pressure of the squeezed state can drive parametric resonance in specific primordial gravitational wave modes. We demonstrate this growth is negligible for non-relativistic ULDM at matter-radiation equality under the assumption of a power-law squeezing spectrum for masses in the range m ∼ 10^-21-10^-24 eV.

We examine the behaviour of the gauge invariant scalar field perturbations in an analytic inflationary model that transitions from slow-roll to an ultra-slow-roll (USR) phase. We find that the numerical solution of the Mukhanov-Sasaki equation is well described by Hamilton-Jacobi (HJ) theory, as long as the appropriate branches of the Hamilton-Jacobi solutions are invoked: modes that exit the horizon during the slow-roll phase evolve into the USR as described by the first HJ branch, up to a subdominant O(k2/H2) correction to the Hamilton-Jacobi prediction for their final amplitude that we compute, indicating the influence of neglected gradient terms. Modes that exit during the USR phase are described by a separate HJ branch once they become sufficiently superhorizon, obtained by the shift (E1, E2) similar or equal to (0, -6 + triangle)-+ (E1, E2) similar or equal to (0, -triangle) and corresponding to a slow-roll solution (very close to de Sitter) supported by the same potential. This transition is similar to the conveyor belt concept put forward in our previous work Phys. Rev. D 104 (2021) 083505 and suggests that the limit E2-+ -6 is unphysical as an asymptotic value for the background/long wavelength solution. We further discuss implications for the validity of the stochastic equations arising from the Hamilton-Jacobi formulation. Our work suggests that if Hamilton-Jacobi attractors are appropriately used, they can successfully describe the dynamics of long wavelength inflationary inhomogeneities for potentials with USR regions.

We consider the gravitational Noether-Ward identities for the evolution of general metric perturbations on quantum matter backgrounds. In this work we consider Einstein's gravity covariantly coupled to a massive, non-minimally coupled, quantum scalar field in general curved backgrounds. We find that each term in the equation of motion for gravitational perturbations satisfies its own Noether-Ward identity. Even though each term is non-transverse, the whole equation of motion maintains transversality. In particular, each counterterm needed to renormalize the graviton self-energy satisfies its own Noether identity, and we derive the explicit form for each. Finally, in order to understand how the Noether-Ward identities are affected by the definition of the metric perturbation, we consider two inequivalent definitions of metric perturbations and derive the Noether-Ward identities for both definitions. This implies that there are Noether-Ward identities for every definition of the metric perturbation.

We study the dynamics of linear gravitational perturbations on cosmological backgrounds of massive fermionic fields. We observe that, when gravitational and matter action are expanded to quadratic order in gravitational perturbations on cosmological backgrounds, the graviton appears to have an off-shell mass. We derive a consistent set of two equations for the evolution of linear classical and quantum gravitational perturbations on general cosmological backgrounds, and demonstrate that the graviton mass disappears at the level of equations of motion (on-shell). In this work we consider a Universe whose expansion is driven by the one-loop quantum backreaction of fermions, and dynamical gravitons that evolve on that same background. These equations govern the evolution of linear gravitational perturbations on general cosmological matter backgrounds. A concrete one-loop calculation is performed for the simple case of massive Dirac fermions when the temperature of the cosmological fluid changes adiabatically when compared with the expansion rate of the Universe.

The fact that graviton propagator contains not only one but two tensorial components excludes a unique definition of the running behavior of the gravitational constant, while at low energies gravitation is characterized solely by Newton’s constant. How these two facts are reconciled when massive quantum fields are present remains unanswered. In this work, by non-minimally coupling gravity to a one-loop massive scalar, we show that this potential conflict is resolved by the non-trivial equivalence between the residues of the two propagator components. Such equivalence is based on a hidden connection between the spin-2 and spin-0 sectors of the propagator. It is verified that this connection also makes the two quantum-corrected gravitational potentials be characterized by the same gravitational constant at large distances. In addition, we find that the potentials in our case as well as the quantum-corrected Coulomb potential can be expressed concisely in a unified formulation. By comparing these results with experiments, we establish a new upper bound on the magnitude of the non-minimal coupling parameter ξ.

Dependence on the graviton gauge enters the conventional effective field equations because they fail to account for quantum gravitational correlations with the source which excites the effective field and with the observer who measures it. Including these correlations has been shown to eliminate gauge dependence in flat space background. We generalize the technique to de Sitter background for the case of the 1-loop graviton corrections to the exchange potential of a massless, minimally coupled scalar.

The large scale geometry of the late Universe can be decomposed as R$\times {\Sigma}_3$, where R stands for cosmic time and ${\Sigma}_3$ is the three dimensional spatial manifold. We conjecture that the spatial geometry of the Universe's spatial section ${\Sigma}_3$ conforms with the Thurston-Perelman theorem, according to which the geometry of $\Sigma_3$ 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 thus-created 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.

We derive the quantum effective action up to second order in gradients and up to two-loop order for an interacting scalar field theory. This expansion of the effective action is useful to study problems in cosmological settings where spatial or time gradients are important, such as bubble nucleation in first-order phase transitions. Assuming spacetime dependent background fields, we work in Wigner space and perform a midpoint gradient expansion, which is consistent with the equations of motion satisfied by the propagator. In particular, we consider the fact that the propagator is non-trivially constrained by an additional equation of motion, obtained from symmetry requirements. At one-loop order, we show the calculations for the case of a single scalar field and then generalise the result to the multi-field case. While we find a vanishing result in the single field case, the one-loop second-order gradient corrections can be significant when considering multiple fields. As an example, we apply our result to a simple toy model of two scalar fields with canonical kinetic terms and mass mixing at tree-level. Finally, we calculate the two-loop one-particle irreducible (1PI) effective action in the single scalar field case, and obtain a nonrenormalisable result. The theory is rendered renormalisable by adding two-particle irreducible (2PI) counterterms, making the 2PI formalism the right framework for renormalization when resummed 1PI two-point functions are used in perturbation theory.

Photon propagator for power-law inflation is considered in the general covariant gauges within the canonical quantization formalism. Photon mode functions in covariant gauges are considerably more complicated than their scalar counterparts, except for the special choice of the gauge-fixing parameter we call the simple covariant gauge. We explicitly construct the position space photon propagator in the simple covariant gauge, and find the result considerably more complicated than its scalar counterpart. This is because of the need for explicitly inverting the Laplace operator acting on the scalar propagator, which results in Appell’s fourth function. Our propagator correctly reproduces the de Sitter and flat space limits. We use this propagator to compute two simple observables: the off-coincident field strength-field strength correlator and the energy-momentum tensor, both of which yield consistent results. As a spinoff of our computation we also give the exact expression for the Coulomb gauge propagator in power-law inflation in arbitrary dimensions.

We firstly generalize the massive scalar propagator for planar gravitational waves propagating on Minkowski space obtained recently in Ref. [1]. We then use this propagator to study the response of a freely falling Unruh-DeWitt detector to a gravitational wave background. We find that a freely falling detector completely cancels the effect of the deformation of the invariant distance induced by the gravitational waves, such that the only effect comes from an increased average size of scalar field vacuum fluctuations, the origin of which can be traced back to the change of the surface in which the gravitational waves fluctuate. The effect originates from the quantum interference between propagation on off-shell detector's trajectories which probe different spatial gravitational potential induced by the gravitational backreaction from gravitational waves, and it is therefore purely quantum. When resummed over classical graviton insertions, gravitational waves generate cuts on the imaginary axis of the complex $Δτ$-plane (where $Δτ= τ-τ'$ denotes the difference of proper times), and the discontinuity across these cuts is responsible for a continuum of energy transitions induced in the Unruh-DeWitt detector. Not surprisingly, we find that the detector's transition rate is exponentially suppressed with increasing energy and the mass of the scalar field. What is surprising, however, is that the transition rate is a non-analytic function of the gravitational field strain. This means that, no matter how small is the gravitational field amplitude, expanding in powers of the gravitational field strain cannot approximate well the detector's transition rate.

We formulate gauge theories on noncompact Lorentzian manifolds. For definiteness we choose an SO(1,4) gauge theory -- the isometry group of the five dimensional Minkowski space. We make use of the natural inner product to construct the Yang-Mills gauge action on four dimensional spacetime, on which the natural tetrad and metric are induced, thus breaking the symmetry to that of general relativity. In the low energy limit -- if a suitable gauge field condensate develops -- the theory reduces to the Cartan-Einstein gravity, which harbors nondynamical torsion, and is consistent with all observations. We also discuss how to couple our gauge theory of gravity to scalar and vector matter. The Hamiltonian analysis shows that the theory possesses no Ostrogradsky instabilities, however it harbors a kinetic instability. We conjecture that such a kinetic instability can be removed either by generalizing the theory to the nonlinear Born-Infeld theory, or by constraining the kinetic instability. This work is an attempt to formulate gravity as a unitary, renormalizable gauge theory without instabilities, in which the fundamental propagating degrees of freedom are in the spin-one tetrad connection.

We consider a free photon field in D-dimensional de Sitter space, and construct its propagator in the general covariant gauge. Canonical quantization is employed to define the system starting from the classical theory. This guarantees that the propagator satisfies both the equation of motion and subsidiary conditions descending from gauge invariance and gauge fixing. We first construct the propagator as a sum-over-modes in momentum space, carefully accounting for symmetry properties of the state. We then derive the position space propagator in a covariant representation, that is our main result. Our conclusions disagree with previous results as we find that the position space photon propagator necessarily breaks de Sitter symmetry, except in the exact transverse gauge limit.

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 $Λ$CDM. 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 $Λ$CDM. 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.

Recent progress on nonlinear sigma models on de Sitter background has permitted the resummation of large inflationary logarithms by combining a variant of Starobinsky's stochastic formalism with a variant of the renormalization group. We reconsider single graviton loop corrections to the photon wave function, and to the Coulomb potential, in light of these developments. Neither of the two 1-loop results have a stochastic explanation, however, the flow of a curvature-dependent field strength renormalization explains their factors of ln(a). We speculate that the factor of ln(Hr) in the Coulomb potential should not be considered as a leading logarithm effect.

We consider the classical attractor regime of the spectator Abelian Higgs model in power-law inflation, and compute the one-loop corrections to its evolution. For computations we utilize dimensional regularization and the propagators in the unitary gauge. The corrections to both the scalar condensate and the energy-momentum tensor exhibit secular ultraviolet contributions, that tend to slow down the rolling of the scalar down its potential, and drive it away from the classical attractor. These corrections need not be suppressed if the U(1) charge is much larger than the scalar self-coupling, which is seen already in flat space. In addition, at late times the secular corrections necessarily invalidate the perturbative loop expansion. We find the late time secular corrections to be captured by the renormalization group, which opens up the possibility to resum them past the breakdown of perturbativity.

The propagator for the massless vector field in de Sitter space cannot maintain de Sitter invariance in the general covaraint gauge, except in the exactly transverse gauge limit. This is due to a previously overlooked Ward-Takahashi identity that the propagator must satisfy. Here we construct the propagator that satisfies all the conditions of a consistently quantized theory. Our solution preserves cosmological symmetries and dilations, but breaks spatial special conformal transformations. The solution amounts to adding a homogeneous de Sitter breaking term to previously reported de Sitter invariant solutions of the propagator equation of motion. Even though the corrections we report pertain to the gauge sector of the linear theory, they are relevant and have to be accounted for when interactions are included.

Abstract We consider single graviton loop corrections to the effective field equation of a massless, minimally coupled scalar on de Sitter background in the simplest gauge. We find a large temporal logarithm in the approach to freeze-in at late times, but no correction to the feeze-in amplitude. We also find a large spatial logarithm (at large distances) in the scalar potential generated by a point source, which can be explained using the renormalization group with one of the higher derivative counterterms regarded as a curvature-dependent field strength renormalization. We discuss how these results set the stage for a project to purge gauge dependence by including quantum gravitational corrections to the source which disturbs the effective field and to the observer who measures it.

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.