Early-universe cosmology
In the past four years, different aspects of primordial cosmology have been investigated.
Recent observations of the gravitational waves emitted by black-hole mergers, together with the apparent persistence of unsolved questions in Cosmology (ranging from the origin of dark matter to the seeding of supermassive black holes in galactic nuclei) have made Primordial Black Holes (PBHs) the subject of increasing attention. If they arise from large quantum fluctuations produced in the early universe, they provide an unprecedented opportunity to constrain the physics at play during the early epoch of cosmic inflation, where the universe underwent a period of accelerated expansion. Since they require large cosmological perturbations to form, they also require to understand physical regimes where quantum backreaction plays an important role in shaping the dynamics of the early universe.
This is why V. Vennin and collaborators have developed the so-called “stochastic-δN formalism” Vennin:2015hra, in which the backreaction of quantum fluctuations onto the expanding background is accounted for in a stochastic effective theory, and the statistics of the resulting cosmological fluctuations can be obtained by solving a first-passage time problem. This has led to the discovery that the distribution function of these perturbations have heavy exponential tails Pattison:2017mbe, that deviate from Gaussian statistics in a non- perturbative way, and which drastically change the expected abundance of PBHs in inflationary models.
Fundamental aspects of the stochastic formalism have also been studied by J. Grain (associate to APC) and V. Vennin, who developed the required tools to extend the formalism to contracting phases, and by J. Serreau and G. Moreau (PhD), who used specific qft techniques to compute various nontrivial observables.
The amplification mechanism that gave rise to PBHs can also take place after inflation, for instance during the phase where the inflaton oscillates at the bottom of its potential. These oscillations trigger a parametric resonant instability in the dynamics of the density contrast (a mechanism known as “metric preheating”), which may eventually collapse into PBHs. This mechanism has been studied by T. Papanikolaou (PhD student at APC between 2018 and 2021) and V. Vennin Martin:2019nuw, and a detailed calculation of the mass fraction of PBHs in this scenario has been obtained by P. Auclair (PhD student at APC over the same period) and V. Vennin. These studies have shown that metric preheating is very efficient at producing ultra-light PBHs, such that the universe could have undergone a period dominated by ultra-light PBHs, before they Hawking evaporate, thereby reheating the Universe. D. Langlois, T. Papanikolaou and V. Vennin have investigated the background of gravitational waves that would be induced by such a PBHs-dominated phase Papanikolaou:2020qtd.
According to the standard cosmological paradigm, cosmological fluctuations originate from the gravitational amplification of quantum fluctuations in the early universe. Although this framework provides predictions in excellent agreement with the data, it raises a number of fundamental issues, such as the va- lidity of the prescription for quantising metric fluctuations, or the emergence of a classical, single configuration for the universe out of a quantum superposition of different states (this is the so-called “meassurement problem” of quantum mechanics, which becomes more severe in the cosmological context since no exterior observer can be identified). This has led V. Vennin and collaborators to work on possible experimental signatures of the quantum origin of cosmological structures Martin:2015qta. Extending tools developed in quantum information theory (such as quantum discord, generalised Bell inequalities, etc) to the realm of quantum cosmological fields, new approaches have thus been proposed to better describe (and hopefully reveal) genuine quantum properties of the primordial fluids. In the same vein, Cosmology can be used to further constrain quantum mechanics and some of its alternative formulations. In particular, V. Vennin and collaborators have shown that models for the dynamical collapse of the wave-function, which incorporate non-linear extension to the Schr¨odinger equation, lead to predictions that are ruled out by current measurements of the cosmic microwave background, at least in their current formulation Martin:2019jye.
Although inflation is often described by a single scalar field, given that it is enough to account for cosmological observations, more degrees of freedom are expected to play a role at the high energies at which inflation proceeds. Those may result into environmental effects such as quantum decoherence, which V. Vennin and collaborators have studied through effective techniques (Lindblad and master equations, etc). In particular, they have identified relevant regimes where decoherence proceeds without substantially affecting the observables of the system Martin:2018zbe.
Finally, our group has developed qft techniques to analytically compute the spectrum of the Fokker-Planck operator in the stochastic formalism that describes the effective infrared dynamics of long wavelength fluctuations of quantum scalar fields. The work Moreau:2019jpn uses a supersymmetric formulation of the stochastic dynamics and computes the lowest eigenvalues, of relevance to various observables of cosmological interest (power spectrum, autocorrelation length/time, decoherence, etc.) both in perturbation theory and in a nonperturbative 1/N expansion, where N is the number of scalar fields. In Moreau:2020gib, we develop specifically the 1/N expansion for the stochastic theory in terms of the Fokker-Planck equation and we obtain the complete spectrum in closed analytical form both at leading and next-to-leading orders.
T. Colas, D. Langlois, G. Moreau, T. Papanikolaou, J. Serreau, V. Vennin
Early-universe cosmology
Most of the dark energy models are based on scalar-tensor theories. It is thus natural to consider dark energy in the most general framework of scalar-tensor theories with a single scalar degree of freedom, known as dhost theories, discov- ered by D. Langlois and K. Noui Langlois:2018dxi.
If one takes into account the constraint on the speed of gravitational waves from the binary neutron star merger GW170817, observed via both gravita- tional and electromagnetic waves, one obtains severe restrictions on dhost the- ories Langlois:2017dyl. Cosmological models within this restricted subclass of theories have been explored Crisostomi:2018bsp.
One can also adopt the viewpoint that gravitational waves from GW170817 correspond to a scale of order 1000 km, much smaller than cosmological scales, and therefore does not necessarily apply to dark energy models. Relaxing the constraints on the speed of gravitational waves, the phenomenology of dark en- ergy models is much richer. Ref. Boumaza:2020klg provides an example where the transition between a matter-dominated era and a phase of accelerated ex- pansion can be studied.
An important ingredient for the viability of dark energy models is the linear stability of the background solution. In order to examine this aspect, we have extended the framework of the Effective Theory of Dark Energy to dhost the- ories Langlois:2017mxy, thus providing a powerful tool to study cosmological perturbations within a vast class of dark energy models.
D. Langlois, K. Noui