## Research

Below is a summary of my past and current research lines, including a brief description.

#### Inflation

Our Universe at large scales is flat (no spatial curvature), homogeneous (uniform with respect to position) and isotropic (uniform independently of the viewing angle); the Cosmic Microwave Background (CMB) has the same temperature throughout the sky in one part in $10^{-5}$. When we ask ourselves if our Universe could have evolved to its current state under generic initial conditions at very early times, the answer is a resounding NO. Assuming that we can extrapolate arbitrarily back in time the Standard Models of particle physics and cosmology, one finds that, unless the Universe was tuned to be perfectly flat to one part in $10^{-57}$, it would have recolapsed or become extremely diluted very quickly. Also, the CMB would have been formed out of $10^5$ causally disconnected patches, in clear contradiction with observations.

One answer to this problem is inflation: an epoch of accelerated expansion in the early Universe, in which a small, single, smooth and causally coherent patch can grow to such a size that it easily encompasses the comoving volume that eventually became the entire Universe today. A slowly-rolling scalar field in an approximately flat potential can easily produce a sufficient amount of inflation. Moreover, the quantum fluctuations of the scalar field seed the primordial density perturbations that become first the temperature fluctuations in the CMB, and later the observed matter distribution in the Universe.

My research has been focused on the realization of inflation in supersymmetric models, in particular no-scale supergravity realizations. The supersymmetric framework is natural, as the amplitude of the spectrum of primordial scalar fluctuations requires small parameters in the inflationary potential; in a supersymmetric theory, such parameters are renormalized multiplicatively, keeping quantum corrections under control. Moreover, supergravity provides a natural extension to general relativity which is valid at the large energies present close to the Planck epoch. Together with J. Ellis, K. Olive and D. Nanopoulos (ENO), I have constructed inflationary models which are capable of reproducing the predictions of chaotic quadratic inflation, Starobinsky inflation, or interpolate between both, via multifield models. An interesting outcome is that two-field effects can produce a spectrum of perturbations consistent with the Planck satellite observations even for a nearly quadratic potential, a result ruled out in the single field case. We also explored the connection between supersymmetry breaking and inflation, which could effectively link low-energy accelerator results with the physics of the early Universe. For a summary of our results regarding no-scale models, see our paper.

#### GUT + inflation + neutrinos

The no-scale formalism, itself inspired by the low-energy regime of orbifold compactifications of the heterotic string, also lends itself to include Grand Unified completions of the Standard Model (SM). In a Grand Unified theory, the SM gauge group $SU(3)_c\times SU(2)_L\times U(1)_Y$ is viewed as arising from the spontaneous breaking of a larger (simple) symmetry group, with a single coupling constant.

With ENO and N. Nagata, we built a SO(10) supersymmetric model in which the right-handed neutrino (together with the rest of the Standard Model matter) is embedded in a 16, while the inflaton corresponds to a singlet of the gauge group. The coupling between both fields gives rise to a double-seesaw, with neutrino masses consistent with oscillation experiments and late-time cosmology, related in a non-trivial way with the CMB observables. We are currently exploring the embedding of flipped-SU(5) in no-scale inflation (see the blog entry here).

#### Reheating

The rapid expansion of the Universe during inflation leaves it in a cold and diluted state. At the end of inflation, all the energy density is stored in the coherent oscillations of the inflaton about its minimum. This condensate eventually decays and populates the Universe with very energetic particles; a hot ‘Big-Bang’ if you will. This process is not instantaneous: its duration and the amount of expansion of the Universe during this process (tied together by the effective equation of state) constitute crucial information necessary to connect the currently observed CMB power spectrum with the quantum fluctuations that originated them during inflation (see Liddle and Leach’s paper). The physics of this reheating process are in general complicated, as the decay products interact with each other and with the inflaton immediately after being produced, which results in additional particle production and the eventual thermalization of the relativistic plasma. Even more, the large-amplitude  oscillation of the condensate can resonantly populate other Bose fields, rapidly transferring it energy. This process occurs far away from thermal equilibrium, and therefore it is called preheating. (For an introduction see e.g. KLS)

As the result of my work with ENO and M. Peloso, we have a better understanding of the reheating epoch in no-scale models. The perturbative decay rate to matter and gauge fields, the time-scale of thermalization, the duration of reheating and the implications on CMB observables have been worked out by us. The combination of the Planck data and our results significantly narrows down the allowed range for the tilt $n_s$ of the primordial scalar fluctuation.

#### Stochastic particle production + reheating

Although simple, single field models of inflation can fit the experimental data, their embedding in a more complete particle physics model tends to be quite complex, involving many fields and complicated interactions (even supersymmetric ones). An extreme example corresponds to the so-called ‘trapped’ models, in which the inflaton is slowed down by the continuous production of light particles. Taking a page out of the known formalism for transport phenomena, one can hope to reconstruct the “macroscopic” observables (the power spectrum, etc.) .. by treating the complex microscopic dynamics in a stochastic fashion. More specifically, it has been shown that there is a mathematical equivalence between stochastic particle production in cosmology and electron transport in wires, where instead of random impurities in a conductor, one deals with seemingly random, non-adiabatic scattering events. As the inflaton dumps its energy, the occupation number of the produced particles executes a drifting Brownian motion, described by a Fokker-Planck equation.

Together with M. Amin and his students/collaborators, we attempt to determine if an universal behavior emerges in the evolution of the particle occupation numbers in systems with a large number of scatterings and statistically inequivalent interacting fields. We eventually want to determine how this emergent universality would be reflected in cosmological observables. For further reading, see the canonical reference Amin-Baumann.

#### WIMP and Axion Dark Matter

All astronomical evidence seems to indicate that we can only observe about 5% of the contents of the Universe. The rest of the mass-energy is stored in a pressureless component,transparent to electromagnetic radiation called dark matter, and an all-permeating, negative pressure component that interacts only gravitationally called dark energy. The evidence for the existence of dark matter is overwhelming (CMB, galaxy rotation curves, gravitational lensing, …), but its nature is yet unknown. My research has led me to investigate the physics of two possible candidates, WIMPs and the PQ axion.

The Lightest Supersymmetric Particle (LSP) is a prime candidate for the Weakly Interacting Massive Particle (WIMP) out of which dark matter would be composed: it is stable, it is interacts weakly, and its scattering cross section leads to the correct relic density. Tied to my research in reheating with ENOP, and with J. Evans, I have explored dark matter production scenarios tied (a) to the decay of the supersymmetry breaking modulus in gravity-mediation models, (b) to the decay of the inflaton in no-scale models, (c) to the thermal and non-thermal production of the gravitino during reheating, and (d) in ‘freeze-in’ scenarios through portals (for more info see here or here).

Motivated by problems such as the null results from the LUX WIMP search, or the ‘too-big-to-fail’ problem (see here), the hypothesis that dark matter is composed of ultra-light axions has been recently rekindled. The Peccei-Quinn axion was originally introduced as an additional real, scalar extra degree of freedom necessary to address the strong CP problem. Its tiny mass and couplings, consistent with the observed dark matter relic density, make it also one of the favored dark matter candidates. With M. Amin, E. Lim and collaborators, we are currently exploring the dynamics and gravitational wave signatures of quasi-solitonic clumps of axion dark matter, interacting with each other or with black holes. For more info see the blog entry or the Hui et. al. review.

#### Baryogenesis

If the Universe started with a ‘bang’, it is natural to expect that an equal amount of matter and antimatter had been created. Why didn’t all the produced matter annihilated with the antimatter? If by some mechanism matter and antimatter were separated, what then happened to the antimatter? There is no evidence of the existence of a significant amount of antimatter in the Universe, which implies that a mechanism producing an imbalance between the number of particles and antiparticles must have been at work in the early Universe; after annihilations only some leftover matter remained. The production of such an imbalance is called baryogenesis. Together with K. Olive, we have constructed viable baryogenesis mechanisms in supergravity by exciting a lepton-number-violating flat direction during inflation, which eventually produces a lepton asymmetry through its decay, and a baryon asymmetry through sphaleron processes (the so-called Affleck-Dine mechanism, see e.g. this review).

#### Lorentz symmetry violation

The foundation upon which quantum field theory and general relativity are built is Lorentz invariance, the fact that the laws of physics stay the same for all observers that are moving with respect to one another with a uniform velocity. Nevertheless, quantum gravitational models beyond GR can lead to low energy “relic signatures” of quantum gravitational effects, among which the spontaneous breaking of the Lorentz symmetry is one. The magnitude of this breaking must be minuscule not to clash with the current experimental bounds, but it can be searched by high precision optical experiments, as it manifests itself as a correction to Maxwell’s equations, leading to non-standard dispersion relations or birefringence of light propagating in the vacuum; these effects can also potentially leave an imprint on the CMB. With C. Escobar, we studied the consequences of LSV at finite temperatures, finding corrections to the black-body radiation law and a cosmological thermal history consistent with the standard scenario. For more info, check out A. Kostelecky’s web page. LSV in the news.

#### Exact solvability in quantum mechanics

The study of an N dimensional system in classical mechanics is greatly simplified if there exist N conserved quantities; that is, N functions of the position and momenta that commute in the Poisson sense with the Hamiltonian of the system, which are therefore constant in time. When this is the case, the equations of motion can be exactly solved by integration (the Liouville-Arnold theorem). There is no parallel (yet) to this result in quantum mechanics; the knowledge of the integrals of motion does not guarantee that the the entire spectrum can be determined exactly. Nevertheless, most (if not all) known quantum integrable systems are also exactly solvable. As my masters and PhD work with A. Turbiner and J. C. López-Vieyra, we solved a family of (super)integrable Calogero-Moser-Sutherland-like models associated with crystallographic ($E_{6,7,8}$) and non-crystallographic ($H_{3,4}$) root systems, showing that the spectrum and the eigenfunctions can be found in terms of invariant polynomials of a hidden algebra of differential operators. We believe that the connection hidden algebra−integrals of motion could be a step toward the quantum L-A theorem. For a brief technical review see this paper or this video.