arXiv subjects

Massimo Giovannini

Publications and source records attributed to Massimo Giovannini.

At least 19 recordsLinked to original sources

arXiv2026

Hanbury-Brown Twiss effect, squeezed gravitons and the photon correlations

Unlike the gravitational waves classically generated by moving macroscopic masses, the diffuse backgrounds of gravitons originate most likely from zero-point fluctuations of the gravitational field amplified by the evolution of the space-time curvature. The resulting entangled states lead to specific second-order correlation effects that could be eventually detected. For a quantitative analysis of this empirical expectation we scrutinize the interactions between the cosmic gravitons and the fundamental mode of a quantized electromagnetic field confined inside a closed optical resonator with perfectly-reflecting walls. We show that the Hanbury-Brown Twiss correlations of the photons are insensitive to the degrees of second-order coherence of the gravitons even barring for the exceedingly small couplings of the problem. Since the degree of second-order coherence of the photons does not reflect the correlation properties of the gravitons, the statistical properties of the gravitons (and their super-Poissonian statistics) cannot be inferred, even in principle, from the intensity correlations of the cavity modes.

hep-th↗

arXiv2026

The initial states of high frequency gravitons

After distinguishing the role of classical and quantum inhomogeneities in cosmological backgrounds, we constrain the initial states of the relic gravitons as soon as the different wavelengths of the spectrum cross the comoving Hubble radius, without any reference to earlier timescales. According to this pragmatic perspective the quantum states with finite energy density at the crossing time consistently affect the two-point functions and the related power spectra. An initial state different from the vacuum turns out to be marginally permitted in the low frequency range (associated with the largest observable wavelengths that crossed the comoving Hubble radius) while the intermediate and high frequency domains of the spectrum are populated by the gravitons produced from the vacuum. The non classical correlations are expected to dominate between the kHz and the THz since in this region gravitons are produced quantum mechanically with a negligible contribution from the initial state.

gr-qc↗

arXiv2025

Invisible gravitons and large-scale magnetism

The large-scale limits on the relic signals of gravitational radiation complement the bounds coming from the interferometric detectors (in the audio band) and from the pulsar timing arrays (in the nHz range). Within this inclusive perspective the spectral energy density of the gravitons is sharply suppressed in the aHz region even though the high frequency signal can be comparatively much larger both in the kHz and GHz domains. For there are no direct tests on the expansion rate prior to the formation of the light nuclei, a modified postinflationary timeline affects the total number of $e$-folds and additionally suppresses the tensor to scalar ratio by making the relic signals effectively invisible in the aHz range. The expansion rate prior to nucleosynthesis is further bounded by the evolution of the hypercharge field and the large-scale magnetism also constrains the decelerated expansion rate. The magnetogenesis requirements are compatible with a potentially detectable spectral energy density of the relic gravitons between the MHz and the THz while the tensor to scalar ratio remains suppressed in the aHz region. A maximum of the spectral energy density of the gravitons in the audio domain leads instead to a larger magnetic field when the scale of the gravitational collapse of the protogalaxy (of the order of the Mpc) gets comparable with the Hubble radius before equality. Along a converse viewpoint the results obtained here imply that a long decelerated stage expanding faster than radiation does not affect the high frequency range but reduces the effective number of $e$-folds by so enhancing the tensor to scalar ratio, possibly beyond its observational limit.

astro-ph.CO↗

arXiv2025

The multiplicity distributions of the high frequency gravitons

When the gravitons are created thanks to the variation of the space-time curvature the multiplicity distributions quantify the probability of producing a given number of species around the average occupation numbers of the underlying multiparticle states. The multiplicities of the relic gravitons are infinitely divisible and their analytical expressions encompass, in different regions of the physical parameters, the Poisson, Bose-Einstein, Gamma and Pascal probability distributions. Depending upon the post-inflationary timelines, the averaged multiplicities are controlled by the range of the comoving frequencies and they can be much larger in the GHz region than in the aHz domain where the temperature and polarization anisotropies of the microwave background set strict limits on the spectral energy density of the relic gravitons. Thanks to the absolute upper bound on the maximal frequency of the gravitons we can acknowledge that the averaged multiplicities are exponentially suppressed above the THz, where only few pairs of gravitons are independently created from the vacuum. The statistical properties of the produced particles can be finally interpreted in the light of the second-order interference effects and this perspective is quantitatively scrutinized by analyzing the associated quantum sensitivities. For putative instruments reaching spectral amplitudes ${\mathcal O}(10^{-35})/\sqrt{\mathrm{Hz}}$ in the MHz or GHz bands, the Bose-Einstein correlations could be used to probe the properties of cosmic gravitons and their super-Poissonian statistics. Both from the theoretical and observational viewpoint it is unjustified to require the same sensitivities (e.g. ${\mathcal O}(10^{-21})/\sqrt{\mathrm{Hz}}$) in the kHz and GHz domains.

hep-th↗

arXiv2025

Entropy bounds from quantum thermodynamics

Within an inherently classical perspective, there is always an unavoidable energy cost associated with the information deletion and this common lore is at the heart of the Landauer's conjecture that does not impose, per se, any relevant limit on the information acquisition. Although such a mindset should generally apply to systems of any size, its quantum mechanical implications are particularly intriguing and, for this reason, we examine here a minimal physical structure where the system and the environment are described, respectively, by a pair of quantum oscillators coupled by an appropriate Hermitian interaction able to amplify the entropy of the initial state. Since at the onset of the dynamical evolution the system is originally in a pure state, its entropy variation is always positive semidefinite and the Landauer's conjecture should not impose any constraint. Nonetheless, provided the quantum amplification is effective, it turns out that the entropy variation of the system always undershoots the heat transferred to the environment. When the initial thermal state of the environment is characterized by a chemical potential, the entropy growth is bounded both by the particles and by the heat flowing to the environment. The limits deduced in the quantum thermodynamical framework are also scrutinized from a field theory standpoint where species of different spins are copiously produced (especially in a cosmological context) thanks to the rapid variation of the space-time curvature.

quant-ph↗

arXiv2025

Ultra-high frequency spikes of relic gravitons

The maximal frequency domain of the cosmic gravitons falls in the THz region where, without conflicting with the existing phenomenological bounds, only few particles with opposite (comoving) three-momenta are produced. Although any reliable scrutiny of the ultra-high frequency spikes should include all the sources of late-time suppression at lower and intermediate frequencies, some relevant properties of the averaged multiplicities and of the spectral energy density can be derived within a reduced set of approximations that may become invalid as the frequency decreases well below the Hz. The accuracy of these concurrent approaches is assessed from the properties of the transition matrix that relates the late-time spectra to the values of the mode functions during an inflationary stage. In the obtained framework the bounds on the post-inflationary expansion rate are swiftly deduced and compare quite well with the ones including a more faithful numerical treatment. It also follows that the timeline of the post-inflationary expansion rate might be observationally accessible, in the years to come, provided the electromechanical detectors (like microwave cavities or waveguides) operating between the MHz and the THz shall eventually reach sensitivities in the chirp amplitudes which are (at least) twelve orders of magnitude smaller than the ones experimentally attainable in the audio band (i.e. between few Hz and the kHz).

gr-qc↗

arXiv2024

Gravitational wave astronomy and the expansion history of the Universe

The timeline of the expansion rate ultimately defines the interplay between high energy physics, astrophysics and cosmology. The guiding theme of this topical review is provided by the scrutiny of the early history of the space-time curvature through the diffuse backgrounds of gravitational radiation that are sensitive to all the stages of the evolution of the plasma. Due to their broad spectrum (extending from the aHz region to the THz domain) they bridge the macroworld described by general relativity and the microworld of the fundamental constituents of matter. It is argued that during the next score year the analysis of the relic gravitons may infirm or confirm the current paradigm where a radiation plasma is assumed to dominate the whole post-inflationary epoch. The role of high frequency and ultra-high frequency signals between the MHz and the THz is emphasized in the perspective of quantum sensing. The multiparticle final state of the relic gravitons and its macroscopic quantumness is also discussed with particular attention to the interplay between the entanglement entropy and the maximal frequency of the spectrum.

gr-qc↗

arXiv2024

Quantum amplification, relic gravitons and Landauer's conjecture

According to the microscopic formulation of Landauer's principle, when information is deleted the Von Neumann entropy of the system gets reduced with a corresponding energy cost. Although within the same perspective the growth of the entropy should remain unconstrained we show that during quantum amplification the heat flow does restrict the increase of the Von Neumann entropy. When applied to the case of relic gravitons (with frequencies between the aHz region and the THz domain) the bounds obtained here set a limit on initial thermal gravitons and on the total duration of inflation.

hep-th↗

arXiv2024

Quantumness of relic gravitons

Since the relic gravitons are produced in entangled states of opposite (comoving) three-momenta, their distributions and their averaged multiplicities must determine the maximal frequency of the spectrum above which the created pairs are exponentially suppressed. The absolute upper bound on the maximal frequency derived in this manner coincides with the THz domain and does not rely on the details of the cosmological scenario. The THz limit also translates into a constraint of the order of $10^{-33}$ on the minimal chirp amplitudes that should be effectively reached by all classes of hypothetical detectors aiming at the direct scrutiny of a signal in the frequency domain that encompasses the MHz and the GHz bands. The obtained high-frequency limit is deeply rooted in the quantumness of the produced gravitons whose multiparticle final sates are macroscopic but always non-classical. Since the unitary evolution preserves their coherence, the quantumness of the gravitons can be associated with an entanglement entropy that is associated with the loss of the complete information on the underlying quantum field. It turns out that the reduction of the density matrix in different bases leads to the same Von Neumann entropy whose integral over all the modes of the spectrum is dominated by the maximal frequency. Thanks to the THz bound the total integrated entropy of the gravitons can be comparable with the cosmic microwave background entropy but not larger. Besides the well known cosmological implications, we then suggest that a potential detection of gravitons between the MHz and the THz may therefore represent a direct evidence of macroscopic quantum states associated with the gravitational field.

hep-th↗

arXiv2024

Relic gravitons and non-stationary processes

Stationary processes do not accurately describe the diffuse backgrounds of relic gravitons whose correlations are homogeneous in space (i.e. only dependent upon the distance between the two spatial locations) but not in time. The symmetries of the autocorrelations ultimately reflect the quantum mechanical origin of the diffuse backgrounds and lead to non-stationary observables at late time. In particular, large oscillations are believed to arise in the spectral energy density that is customarily (but approximately) related to the tensor power spectrum. When the full expression of the spectral energy density is employed the amplitudes of oscillation are instead suppressed in the large-scale limit and the non-stationary features of the late-time signal practically disappear. For similar reasons the relations between the spectral energy density and the spectral amplitude are ambiguous in the presence of non-stationary features. While it is debatable if the non-stationary features are (or will be) directly detectable, we argue that the spectral amplitude following from the Wiener-Khintchine theorem is generally inappropriate for a consistent description of the relic signal. Nevertheless the strong oscillatory behaviour of the late-time observables is naturally smeared out provided the spectral energy density is selected as pivotal variable.

gr-qc↗

arXiv2024

Fuzzy Bounces

We observe that the energy and the enthalpy densities can be smeared by two fudge factors that are constrained by the contracted Bianchi identities. Depending on the analytic properties of the smearing functions the underlying cosmological solutions belong to two physically different classes, namely the bounces of the scale factor and the curvature bounces. While the curvature bounces are naturally compatible with a stage of accelerated expansion, the bounces of the scale factor demand an early phase of accelerated contraction even if a short inflationary stage may arise prior to the decelerated regime. Despite the regularity of the underlying solutions, gradient instabilities and singularities do occasionally appear in the evolution of curvature inhomogeneities. After deducing the specific criteria behind these occurrences, the background-independent conclusions are corroborated by a series of concrete examples associated with different forms of the smearing functions. The evolution of the curvature inhomogeneities restricts the ranges of the solutions that turn out to be unsuitable even for a limited description of the pre-inflationary initial data. The same observation holds in the case of the gauge-invariant evolution of the matter density contrast. It is however not excluded that a class of scenarios (mainly associated with the curvature bounces) could indeed avoid the potential instabilities. All in all the present analysis explore a general approach whose results are relevant in all the contexts where bouncing solutions are invoked either as complementary or as alternative to the conventional inflationary scenarios.

gr-qc↗

arXiv2024

Relic gravitons and pulsar timing arrays: a theoretical viewpoint

During the last three years the pulsar timing arrays reported a series of repeated evidences of gravitational radiation (with stochastically distributed Fourier amplitudes) at a benchmark frequency of the order of $30$ nHz and characterized by spectral energy densities (in critical units) ranging between $10^{-8}$ and $10^{-9}$. While it is still unclear whether or not these effects are just a consequence of the pristine variation of the space-time curvature, the nature of the underlying physical processes would suggest that the spectral energy density of the relic gravitons in the nHz domain may only depend on the evolution of the comoving horizon at late, intermediate and early times. Along this systematic perspective we first consider the most conventional option, namely a post-inflationary modification of the expansion rate. Given the present constraints on the relic graviton backgrounds, we then show that such a late-time effect is unable to produce the desired hump in the nHz region. We then analyze a modified exit of the relevant wavelengths as it may happen when the gravitons inherit an effective refractive index from the interactions with the geometry. A relatively short inflationary phase leads, in this case, to an excess in the nHz region even if the observational data coming from competing experiments do not pin down exactly the same regions in the parameter space. We finally examine an early stage of increasing curvature and argue that it is not compatible with the observed spectral energy density unless the wavelengths crossing the comoving horizon at early times reenter in a decelerated stage not dominated by radiation.

gr-qc↗

arXiv2023

The maximal frequency of cosmic gravitons

We show that the maximal frequency of cosmic gravitons must not exceed the THz domain. From a classical viewpoint, both in conventional inflationary scenarios and in bouncing models the largest frequency of the spectrum overshoots the MHz band even if its specific signature is model dependent. According to a quantum mechanical perspective the maximal frequency is instead associated with the range of energies where a single pair of gravitons with opposite (comoving) three-momenta is produced. The upper limit on the largest frequency determines the minimal chirp amplitude [typically ${\mathcal O}(10^{-32})$] required for a direct detection of a cosmic signal in the THz band. Below this limiting frequency the minimal chirp amplitude can be enhanced so that the optimal range ultimately depends on the physical properties of the diffuse backgrounds. In case a hypothetical instrument (at present just a figment of a hopeful imagination) would reach chirp amplitudes down to ${\mathcal O}(10^{-30})$ in the MHz or GHz bands, the Bose-Einstein correlations could be used to probe the properties of cosmic gravitons and their super-Poissonian statistics.

gr-qc↗

arXiv2023

The invisible low-frequency gravitons and the audio band

The low-frequency gravitons correspond to typical wavelengths that left the Hubble radius during the early inflationary stages of expansion and reentered after matter radiation equality. Consequently the temperature and the polarization anisotropies of the cosmic microwave background constrain the tensor-to-scalar-ratio in the aHz region but since the audio band and the MHz domain are sensitive to the post-inflationary expansion rate, the low-frequency determinations of the tensor-to-scalar-ratio can be combined with the high-frequency constraints. In this framework we examine the possibility that the low-frequency gravitons remain invisible in the aHz region but are still potentially detectable at much higher frequencies. Because the number of $e$-folds associated with the exit of the cosmic microwave background wavelengths depends both on the slow-roll parameters and on the total expansion rate after inflation, this approach leads to a set of lower bounds on the tensor-to-scalar-ratio.

gr-qc↗

arXiv2023

Relic gravitons and high-frequency detectors

Cosmic gravitons are expected in the MHz-GHz regions that are currently unreachable by the operating wide-band interferometers and where various classes of electromechanical detectors have been proposed through the years. The minimal chirp amplitude detectable by these instruments is often set on the basis of the sensitivities reachable by the detectors currently operating in the audio band. By combining the observations of the pulsar timing arrays, the limits from wide-band detectors and the other phenomenological bounds we show that this requirement is far too generous and even misleading since the actual detection of relic gravitons well above the kHz would demand chirp and spectral amplitudes that are ten or even fifteen orders of magnitude smaller than the ones currently achievable in the audio band, for the same classes of stochastic sources. We then examine more closely the potential high-frequency signals and show that the sensitivity in the chirp and spectral amplitudes must be even smaller than the ones suggested by the direct and indirect constraints on the cosmic gravitons. We finally analyze the high-frequency detectors in the framework of Hanbury-Brown Twiss interferometry and argue that they are actually more essential than the ones operating in the audio band (i.e. between few Hz and few kHz) if we want to investigate the quantumness of the relic gravitons and their associated second-order correlation effects. We suggest, in particular, how the statistical properties of thermal and non-thermal gravitons can be distinguished by studying the corresponding second-order interference effects.

gr-qc↗

arXiv2023

The scaling of primordial gauge fields

The large-scale magnetic fields arising from the quantum mechanical fluctuations of the hypercharge are investigated when the evolution of the gauge coupling is combined with a sufficiently long inflationary stage. In this framework the travelling waves associated with the quantum mechanical initial conditions turn asymptotically into standing waves which are the gauge analog of the Sakharov oscillations. Even if the rate of dilution of the hypermagnetic and hyperelectric fields seems to be superficially smaller than expected from the covariant conservation of the energy-momentum tensor, the standard evolution for wavelengths larger than the Hubble radius fully accounts for this anomalous scaling which is anyway unable to increase the amplitude of the magnetic power spectra after symmetry breaking. An effective amplification of the gauge power spectra may instead occur when the post-inflationary expansion rate is slower than radiation. We stress that the modulations of the gauge power spectra freeze as soon as the relevant wavelengths reenter the Hubble radius and not at the end of inflation. After the Mpc scale crosses the comoving Hubble radius the scaling of the magnetic power spectrum follows from the dominance of the conductivity. From these two observations the late-time values of the magnetic power spectra are accurately computed in the case of a nearly scale-invariant slope and contrasted with the situation where the phases of Sakharov oscillations are not evaluated at horizon crossing but at the end of inflation, i.e. when all the wavelengths relevant for magnetogenesis are still larger than the comoving horizon.

astro-ph.CO↗

arXiv2022

The hypermagnetic power spectra and the phases of Sakharov oscillations

If the gauge fields are amplified from the inflationary vacuum, the quantum mechanical initial data correspond to travelling waves that turn asymptotically into standing waves whose phases only depend on the evolution of the gauge coupling. We point out that these gauge analogs of the Sakharov oscillations are exchanged by the duality symmetry and ultimately constrain both the relative scaling of the hypermagnetic power spectra and their final asymptotic values. Unlike the case of the density contrasts in a relativistic plasma, the standing oscillations never develop since they are eventually overdamped by the finite value of the conductivity as soon as the corresponding modes are comparable with the expansion rates after inflation. We show that the late-time value of the magnetic field is not determined at radiation dominance (and in spite of the value of the wavenumber) but it depends on the moment when the wavelengths (comparable with the Mpc) get of the order of the Hubble radius before equality. This means that the magnetogenesis requirements are only relaxed if the post-inflationary expansion rate is slower than radiation but the opposite is true when the plasma expands faster than radiation and the corresponding power spectra are further suppressed. After combining the present findings with the evolution of the gauge coupling we show that these results are consistent with a magnetogenesis scenario where the gauge coupling is always perturbative during the inflationary stage while, in the dual case, the same requirements cannot be satisfied.

hep-th↗

arXiv2022

Inflation, space-borne interferometers and the expansion history of the Universe

According to the common wisdom, between a fraction of the mHz and few Hz the spectral energy density of the inflationary gravitons can be safely disregarded even assuming the most optimistic sensitivities of the space-borne detectors. In this analysis we show that this conclusion is evaded if, prior to nucleosynthesis, the post-inflationary evolution includes a sequence of stages expanding either faster or slower than radiation. As a consequence, contrary to the conventional lore, it is shown that below a fraction of the Hz the spectral energy density of the relic gravitons may exceed (even by eight orders of magnitude) the signal obtained under the hypothesis of radiation dominance throughout the whole expansion history prior to the formation of light nuclei. Since the slopes and the amplitudes of the spectra specifically reflect both the inflationary dynamics and the subsequent decelerated evolution, it is possible to disentangle the contribution of the relic gravitons from other (late-time) bursts of gravitational radiation associated, for instance, with a putative strongly first-order phase transition at the TeV scale. Hence, any limit on the spectral energy density of the relic gravitons in the mHz range simultaneously constrains the post-inflationary expansion history and the inflationary initial data.

gr-qc↗