My research interests are broad in the field of Astrophysics and Cosmology and change from time to time depending on developments in the field. I do avoid following fashions and tend to do research on what purely interest my intellect. I will work on whatever I think will be the most effective tool to understand the nature of the Universe. I chose cosmology as my research field as I find it the most exciting, data-rich and promising area of human knowledge to unveil the fundamental laws of nature. Another aspect of my research has been my continuous interest in rigorous statistics and, in particular, Bayesian inference to understand data and how, we humans, infer facts about nature.
FOUR MAIN CURRENT RESEARCH INTERESTS ARE:
1.COMPLEXITY: Deep neural nets offer a new route towards understanding the structure of the solutions of many partial differential equations. I have been developing a method based on physics informed neural networks that incorporates significant advances in the algorithmic front of machine learning. One of the outcomes of the approach is the identification of an appropriate set of basis functions for solving a given partial differential equation. This method was recently applied to the solutions of the Burgers equation by training the network for different values of Burgers viscosity. The network discovers that wavelets are the natural basis with scale
relevant parameter for determining complexity. As we reduce the value of viscosity, we are finding a renormalization group
flow from the ultraviolet to the infrared that depends degrees of freedom. I plan to apply this approach to the Navier-Stokes
equations. The role of the renormalization group
in shaping complexity and whether there is any scaling law that we can determine from the neural network solution as
we flow from the ultra-violet to the infrared and we remove degrees of freedom is an important synergy with theoretical
physics. This effort is supported by a Simons Innitiative
2. AGES OF OLD COSMIC OBJECTS: Despite a century of progress, achieving precise and robust cosmic age determinations
remains an open and fundamental problem. I continue to develop a research program aimed at obtaining reliable and
precise ages of the Universe across cosmic time, targeting sub-percent accuracy. This effort will involve advancing stellar
evolution models, with a particular focus on accurately modeling convection (a key challenge to reach the sub-percent
accuracy). By combining modern deep-learning techniques with Bayesian statistical methods, I aim to comprehensively
model and marginalize over all relevant systematic uncertainties. This effort is part of the RedHot Synergy grant.
3. TOWARDS A THEORY OF INFLATION: Inflation, the brief period of exponential expansion in the very early Universe, is widely accepted as a successful phenomenological description of cosmological initial conditions. At the same time, it is often
described as a “paradigm without a theory”: existing inflationary models are highly flexible, rely on free parameters,
and consequently suffer from limited predictability and falsifiability. My research has made concrete progress toward
addressing these shortcomings by developing cosmological frameworks with no free parameters. Notable examples
include Quantum Fisher Cosmology and, more recently, the Inflation without an Inflaton scenario, which demonstrates
how the entire observable Universe can arise from quantum fluctuations of the spacetime metric in de Sitter space, without
introducing additional fields. In parallel, I have shown how the genuinely quantum nature of the early Universe can be
tested with forthcoming observations, opening a pathway to experimental validation of these ideas. These initial advances
now require substantial further development. My plan is to deepen the theoretical foundations of these frameworks by
deriving de Sitter spacetime from more fundamental principles while simultaneously confronting their predictions with
upcoming cosmological data. This effort is funded by Spanish research funds.
4. MULTI-AGENTIC INFERENCE AND AUTOMATED "REASONING: The most exciting development in last couple of years is the possibility that machine-based algoritms can help us to do reasearch by "reasoning" My efforts in this area are represneted by my contribution to Denario o facilitate automated research in multiple fields. Denario is a transformative framework in which AI multi-agent systems become epistemic actors embedded within the scientific method. I believe this could be a paradigm chnaging breakthrough.
To summarize, my research style embraces high-risk, high-gain ideas: I focus on genuinely unsolved problems for which
no solution is known a priori. Looking back at my past research, the contributions I value most are precisely those I did not
anticipate in advance; my most productive research directions have consistently emerged from unexpected conversations, col-
laborative brainstorming, and the exploration of new ideas. Accordingly, over the next five years some of the research avenues
outlined here may prove unfruitful and be set aside. However, this flexibility is a strength rather than a weakness: it creates
the conditions under which genuinely new directions can emerge. By remaining open to discovery and guided by fundamental
questions rather than predetermined outcomes, this program is designed to maximize the likelihood of transformative advances.
SCIENTIFIC ACHIEVEMENTS
The list below sumarizes the main findings about nature I have made during my scientific career. The number in parenthesis corresponds to the article number in the CV publication list:
The Age of the Universe and Cosmological Parameters: The first accurate and precise constraint on the age of the Universe using globular clusters (13.5 Gyr, published in 1995); among the first indications for a cosmological constant using the ages of high-z galaxies and the ages of globular clusters (4, 7, 8, 12, 17). The first reliable and accurate estimate of the ages of high-z galaxies (6, 15, 18). The first accurate constraints on the age of Milky Way disk (20). A new method to directly measure the expansion history of the metric of space time via cosmic chronometers: the cosmic chronometer method (39, 59). I was the first one to introduce the term ``tension" and quantify it regarding the mismatch at high and low-redshift of the $H_0$ (137, 140, 148). A demonstration of the accuracy of the cosmic chronometer method to compute cosmology parameters (158, 159, 171, 177). A new precise and accurate measurement of the age of the universe at the \% level (173, 183, 187, 205, 206, 207). A method to measure $H_0$ from neutrino oscillations (196). A model to explain how minuscule black holes formed during inflation that produce gravitons can remove the Hubble tension (202). I have extended the age-dating technique to local and high-redshift globular clusters (210, 212, 214, 222).
Stellar Populations: The solution of the long standing inverse problem of deriving physical quantities from the integrated light of stellar populations via the MOPED and VESPA algorithms (34, 76). The determination of the ages, metallicities and star formation histories of galaxies from their integrated spectrum using MOPED and VESPA (53, 56, 57, 74, 86).
Stars and the Interstellar Medium: An accurate measurement of the primordial He abundance (46, 78). The first theoretical prediction that the magnetic field in molecular clouds is low (52). The discovery of the nature of Supernova type-Ia progenitors (87, 103). The role of GRBs in life survival in the universe; a lower bound to the value of the cosmological constant (155). A quantitative demonstration of the effect that giant planets can have in biasing the cosmic ladder (182).
Galaxy Formation and Evolution: Among the first parameter-free models for the formation of GCs in the LCDM paradigm (13, 153). The prediction, and later confirmation, of the existence of dark galaxies (16, 40, 178). The prediction of the existence of high-z ($z > 3$) massive elliptical galaxies (24). The observational demonstration of the existence of primordial gas at low redshift ($z \sim 3$) (64). How to perform tomography of the re-ionization epoch (69, 72, 79). A theoretical model for the formation of the first galaxies (141, 143). The theoretical discovery of how galaxies obtain their spin in the hierarchical model of structure via the cosmic web (152). The finding that there are no missing low-mass galaxies in a cosmological volume of 1 Gpc^3 (169).
Large Scale Structure: The first accurate analytical calculation of the non-gaussian mass function of collapsed structures (27). The first hints from the abundance of rare objects of primordial non-gaussian fluctuations (96). The development of analytic methods to compute the large scale structure of the universe (104, 115, 138,144). The development of accurate and exact tools to analyze weak lensing cosmological studies (154, 157, 166). A method to measure in a cosmology-model independent way the standard ruler of the Universe (162).
Neutrino Cosmology: The measurement of neutrino masses and their hierarchy from cosmology (97, 127, 161, 163, 165). A new method to distinguish Dirac from Majorana neutrinos using astronomical observations (197, 207) and new predictions on the shape of neutrino profiles (209). I have also made the first accurate predictions on how the cross-correlatiosn of the cosmic neutrino background look like (215). I have also developed a novel method to measure the cosmic neutrino background using celestial objects (217).
Dark Energy Theory: A dynamical origin to explain the nature of dark energy as a source of momentum exchange with neutrinos (168, 184). Some of the strongest constraints on modifications of gravity, putting these theories under pressure (142, 151, 156, 159, 163, 175, 185).
Dark Matter: The first precise computation of annihilation and profile spikeness of dark matter halo profiles (38). A method to detect the existence of axions from astronomical observations (117, 126). A quantitative demonstration that the existence of dwarf galaxies without dark matter implies that dark matter can only be cold CDM (183).
Early Universe and Theoretical Cosmology (The Quantum Nature of the Universe): An inflation model from pure (super-)symmetry considerations (101,110, 125). The best model independent constraint on the amount of different types of energy densities in the early Universe: no room for early dark energy (164). A method to measure deviations from Einstein gravity at the Planck scale using non-gaussian observations of the CMB (170). A new method to test the early Universe via measurements of the graviton exchange during inflation using the non-gaussian halo power--spectrum (172). A new method to measure the Homogeneity of the Universe for any general metric and independently on the cosmological model: a way to see inside the past light-cone (174). A method to constraint the global curvature of the Universe independent of the cosmology model (167). A new approach based entirely on quantum mechanics to describe the early Universe, including a robust prediction that the tensor-to-scalar ratio must be 0.01 (176, 179, 180). A model independent method to describe quasi de Sitter as a pure non-perturbative quantum gravity phenomenon on exact de Sitter as a result of the quantum phases as described by the quantum Fisher (185, 186, 188, 189, 190, 192, 195). A new insight of why the Universe is exactly spacially flat (201). I have also developed a new picture to observationally test the quantum nature of the Universe (216,224) and a new theory in which the scalar perturbations of the Universe is generated from quantum fluctuations of space-time (211,216).
Statistics and Inference: The invention of the data compression algorithm MOPED(28) and VESPA(79) . The development of rigorous statistical methods to analyse astronomical observations and reduce the effect of systematic errors (120). A new parameterization of the cosmic microwave background that opened the door to fast cosmological parameter estimation (43). A theoretical method to better design CMB polarization experiments (63).
Holography, Gravitational Waves and the Early Universe: I have developed a new approach to study singularities and strongly coupled field theories to understand also phase transitions in the early Universe as well as the state of matter in neutron stars collisions (208).
Computational methods: I have developed new algorithms in the field of machine learning to solve differential equations (PINNs). In particular, I have found new schemes to facilitate the search for solutions in NN with ultra-complex morphology that contains multiple maxima/minima and inflection points. This has wide ranging applications in the field of ML (213). I have published a textbook on the subject (4, 5).
AI, Robotization and Society: I have written two books on the impact of robotization and AI on society and democracy as well as numerous articles (238-278) on the same subject.
Complexity: I have developed new methods to understand complexity, In particular how to characterized the solution space of non-linear PDEs. This is done in the context of both astrophysical phenomena, game theory and language models. In particular: a new method to analyze and classify the solutions of highly complex PDEs (218) or stochastic partial differential equations (231).
Multi-Agent LLM/AI inference: I am an active member of the Denario project to facilitate automated research in multiple fields. Denario is a transformative framework in which AI multi-agent systems become epistemic actors embedded within the scientific method.