Applicants interested in early universe cosmology (cosmic inflation, reheating, cosmic defects…), CMB, large scale structures, gravitational waves cosmology, as well as data analysis for current and future cosmological observations (CMB-S4, Euclid, LiteBird, LISA…), are particularly encouraged to apply. A summary of our research interests can be consulted online.
Appointment is available for two years. Please notice that applicants should have obtained their PhD no longer than 5 years before the starting date of the fellowship, plus one year of allowance for parenthood.
Letters of application (including a curriculum vitae, a list of publications, a brief statement of research interests) and at least two recommendation letters from senior scientists should be submitted on-line, by the 28th of January 2024, at:
https://cp3.irmp.ucl.ac.be/job/94
For more information, or postal applications, please contact:
christophe.ringeval@uclouvain.be
Cosmology, Universe and Relativity at Louvain
Institute of Mathematics and Physics
Louvain University
2, Chemin du Cyclotron
1348 Louvain-la-Neuve
Belgium
Applicants with expertises in cosmic inflation, large scale structures, data analysis and Bayesian inference, skilled in computing and analytics, are particularly encouraged to apply.
The position is supported by the Belgium Euclid Science Exploitation ESA-Prodex research program which unifies expertises between Ugent (Gent), ULiege (Liège), ULB (Brussels) and UCLouvain (Louvain-la-Neuve) universities. There will be close collaborations between these groups, computing and travelling support are excellent.
Appointment is available for three years.
Letters of application (including a curriculum vitae, a list of publications, a brief statement of research interests) and at least two recommendation letters from senior scientists should be submitted on-line, by the 28th of January 2024, at:
https://cp3.irmp.ucl.ac.be/job/95
For more information, or postal applications, please contact:
christophe.ringeval@uclouvain.be
Cosmology, Universe and Relativity at Louvain
Institute of Mathematics and Physics
Louvain University
2, Chemin du Cyclotron
1348 Louvain-la-Neuve
Belgium
It is a common Cosmologist’s intuition that cosmological fluctuations, the tiny perturbations of amplitude \(10^{-5}\) at the origin of galaxies, should induce some kind of noise on the cosmological parameters. Is this quantifiable? Are super-Hubble cosmological perturbations having an effect at all?
In Ref. [1], we show that arbitrarily long perturbations have an observable effect. More precisely, the gradient and Laplacian of these fluctuations are dynamically creating a spatial curvature in the homogeneous and isotropic metric of local observers. In the following picture, we sketch how one of these modes, having a wavelength much larger than the observer’s Hubble radius, can be “felt” through its gradient.
It is not a few Hubble-sized fluctuations that contribute, but an infinite number of super-Hubble modes, all those having wavelength larger than our observable universe. Denoting by \(K\) the curvature of the FLRW spatial sections, and \(\xi\) the sum of these constant modes, we find
\[K = -\frac{2}{3} \Delta \xi - \frac{1}{3} \left(\nabla \xi \right)^2.\]However, because fluctuations are, by definition, of random nature, we cannot predict a definite value for the curvature density parameter \(\Omega_\mathrm{K_0}\). This one is now promoted to a stochastic variable. Even though the sum of all super-Hubble modes averages to zero, i.e. \(\langle \xi \rangle = 0\), we predict, for the standard Gaussian and scale-invariant cosmological perturbations, a very small non-vanishing value
\[\langle \Omega_\mathrm{K_0} \rangle = -\frac{\langle K e^{-2\xi} \rangle}{a_0^2 H_0^2} = \frac{5}{6} \mathcal{P}_* \simeq 1.7 \times 10^{-9}.\]More importantly, because \(\Omega_\mathrm{K_0}\) is a stochastic variable, it also fluctuates and its realizations are, in fact, dictated by its standard deviation
\[\sqrt{\langle{\Omega_\mathrm{K_0}^2}\rangle-\langle{\Omega_\mathrm{K_0}}\rangle^2} \simeq \dfrac{1}{3} \sqrt{\mathcal{P}_*} \simeq 1.5 \times 10^{-5}.\]This is the typical value that any observer will measure at any epoch during the cosmic history.
But there is more. The spatial curvature of our local Hubble patch is thus a measurable number that can tell us what is going on on the largest possible length scales of the Universe, length scales that are much larger than our Hubble volume. What if the infinite sum of very large wavelength modes, \(\xi\) here, is no longer a small quantity? Such a situation could very well be happening if the Universe has experienced a period of stochastic inflation in its infancy!
In Ref. [1], we have been able to estimate the full probability distribution function for \(\Omega_\mathrm{K_0}\) when cosmological fluctuations are generated by Cosmic Inflation. If \(\xi\) remains small, it is a slightly distorted Gaussian distribution with a typical width of \(10^{-5}\), as expected. But if inflation last for a long period, enough for \(\xi\) to be of order unity, the distribution becomes highly non-Gaussian, as represented in the following figure (red curve)
In this plot, the black curve is what would be a Gaussian probability distribution with same width. Clearly, large values of \(\Omega_\mathrm{K_0}\) are now much more probable than what one could have naively expected. Are we going to measure a non-vanishing \(\Omega_\mathrm{K_0}\) in the future?
]]>At 2pm, room E349, Bryce Cyr (University of Manchester), will be talking about
In this talk, I will discuss various ways in which distortions to the frequency spectrum of the cosmic microwave background can be used to place constraints on stochastic backgrounds of gravitational waves. After a brief overview of spectral distortion theory, I will show how enhancements to the small-scale primordial power spectrum of curvature perturbations can induce sizeable distortions. Even in the absence of enhancements, a nearly-scale invariant spectrum presents a target well within reach of next generation experiments. Additionally, I will highlight how the presence of primordial tensor modes will also lead to an inevitable (although small) distortion signature. I will then apply this formalism to a model of scalar induced gravitational waves (SIGWs), showcasing how constraints on the primordial scalar power spectrum can be mapped to the gravitational wave parameter space for these models. Time permitting, I will also show our updated formalism can be used to improve constraints on the parameter space of primordial black holes.
]]>At 2pm, room E349, Suvashis Maity (IIT Madras), will be talking about
Recently, there have been efforts to examine the contributions to the scalar power spectrum due to the loops arising from the cubic order terms in the action describing the perturbations, specifically in inflationary scenarios that permit a brief epoch of ultra slow roll (USR). A phase of USR inflation leads to significant observational consequences, such as the copious production of primordial black holes. In this talk, I shall discuss the loop contributions to the scalar power spectrum in scenarios of USR inflation arising due to the quartic order terms in the action describing the scalar perturbations. I shall initially describe the computation of the loop contributions to the scalar power spectrum due to the dominant term in the action at the quartic order. Thereafter, I shall consider a scenario wherein a phase of USR is sandwiched between two stages of slow roll inflation and describe the behavior of the loop contributions in situations involving late, intermediate and early epochs of USR. In the inflationary scenario involving a late phase of USR, for reasonable choices of the parameters, I shall show that the loop corrections are negligible for the entire range of wave numbers. In the intermediate case, the contributions from the loops prove to be scale invariant over large scales, and we find that these contributions can amount to 30% of the power spectrum at the leading order. In the case wherein USR sets in early, we find that the loop contributions could be negative and can dominate the power spectrum at the leading order, which indicates a breakdown of the perturbative expansion. I shall conclude with a brief summary and outlook.
]]>Ce jeudi 29 Juin 2023, plusieurs collaborations internationales en radio-astronomie, NANOGRAV, EPTA, PPTA, InPTA et CPTA, ont annoncé avoir détecté indépendamment un fond stochastique d’ondes gravitationnelles dans une bande de fréquences située autour du milliardième de Hertz. C’est une découverte majeure qui devrait nous permettre d’en apprendre beaucoup sur la formation des galaxies et sur la physique a l’œuvre dans tout l’Univers.
Les contributions de Pierre à la publication de EPTA, Ref. [1], concernent l’analyse des différentes sources cosmologiques possibles, dont les cordes cosmiques, un des domaines d’expertise de CURL.
Le fond stochastique d’ondes gravitationnelles est la superposition de toutes les ondes gravitationnelles émises dans l’univers. Par analogie avec le son, c’est comme si nous avions etendu le brouhaha d’une foule sans toutefois parvenir à distinguer une conversation en particulier. Ce bruit de fond est très intéressant car il donne accès aux propriétés stochastiques et globales de toutes les sources à la fois.
Tout aussi spectaculaire que cette découverte est la méthode utilisée pour trouver ce fond d’ondes gravitationnelles. Point de détecteurs terrestres ou spatiaux, mais des étoiles à neutrons particulières. Une étoile à neutron est le cœur chaud et ulta-dense qu’il reste après qu’une étoile supermassive (entre 10 et 20 fois la masse du Soleil) ait explosé en supernova. La fameuse nébuleuse du Crabe, un rémanent de supernova, contient un pulsar en son centre.
Les réseaux de pulsars millisecondes, ou Pulsar Timing Arrays (PTA) en anglais, utilisent des étoiles à neutrons tournant très rapidement sur elles-même, plusieurs centaines de fois par seconde, qui émettent un fort rayonnement dans la direction de leur axe magnétique. À la manière d’un phare, le pulsar semble avoir une pulsation lorsque ce rayonnement radio se trouve en direction de la Terre.
La pulsation très régulière des pulsars en font des horloges célestes extrêmement précises. En observant ces pulsars pendant plus de vingt ans au moyen de radiotélescopes, et en notant soigneusement les petites irrégularités dans les temps d’arrivée de leur flash, les radioastronomes sont parvenus à mettre en évidence l’existence de ce fond stochastique d’ondes gravitationnelles. En effet, lorsque ces ondes gravitationnelles passent entre la Terre et les pulsars, elles induisent des déformations de l’espace-temps qui laissent une corrélation caractéristique entre les temps d’arrivée des flashs.
Si la nature “onde gravitationnelle” de ce signal est donc établie, plusieurs interprétations sont néanmoins possibles concernant son origine. L’hypothèse présentée comme la plus naturelle est celle d’un fond stochastique dû à des binaires de trous noirs supermassifs. D’autres propositions, comme les cordes cosmiques ou les transitions de phases du premier ordre, permettraient aussi d’expliquer les observations, avec d’importantes conséquences pour notre compréhension des premiers instants de l’Univers.
]]>Le lancement du satellite Euclid (ESA) est prévu pour le 1er juillet 2023 à 17h11 (CEST) depuis Cap Canaveral, à suivre en direct sur l’ESA web TV. D’ici là, une conférence de presse est organisée au Planétarium de Bruxelles, lundi 26 juin à 10h.
]]>The first edition of Encyclopædia Inflationaris was published in Ref. [1] and authored by Jérôme Martin, Christophe and Vincent Vennin. It was built upon the slow-roll models of inflation proposed prior to 2013, the year of the first Planck data release. It contains accurate reheating-consistent slow-roll calculations of the background universe and of the expected scalar and tensor perturbations for all these models. Although it is now often seen as a review, it is a genuine paper as it goes beyond the mere gathering of known results. Indeed, a fair fraction of these models had been studied only under rough approximations, which were not matching the accuracy needed by the Cosmic Microwave Background (CMB) data. The ambition of the project was, and still is, to provide an (almost) exact treatment of single-field inflationary models using only the slow-roll approximation while incorporating the kinematic effects of reheating.
All these results are also incorporated in a public runtime library, ASPIC [2], which has been used in a number of subsequent works. For instance, Bayesian model comparison using the Planck CMB data has been presented in Refs. [3] and [4] while the constraints derived on the reheating epoch have been separately presented in Refs. [5] and [6].
Ten years later Cosmic Inflation remains the most favoured scenario of the early universe [7] but several developments have called for the release of a new edition:
First, at the theoretical level, new models have been proposed. Some of them boil down to one of the functional forms of the inflationary potentials already encoded in ASPIC, in which case they have been added in the relevant sections^{1}. Some other models give rise to new inflationary potentials, and therefore constitute new sections of Encyclopædia Inflationaris, as well as new entries in the ASPIC library. There are 24 such new potential functions in the new edition (here ordered alphabetically): Axion Hilltop Inflation (AHI), Cubicly Corrected Starobinsky Inflation (CCSI),Double Exponential Inflation (DEI), Dual Inflation (DI), Fibre Inflation (FI), Generalized Double Well Inflation (GDWI), Hyperbolic Inflation (HBI), Hybrid Natural Inflation (HNI), Non-Renormalizable Corrected Loop Inflation (NCLI), N-Formalism Inflation (NFI), Non-Minimal Large Field Inflation (NMLFI), Pure Arctan Inflation (PAI), Radiatively Corrected Inflection Point Inflation (RCIPI), Radiatively Corrected Large Field Inflation (RCLFI), String Axion Inflation I (SAII), String Axion Inflation II (SAIII), Super-conformal Alpha Attractor A Inflation (SAAI), T-Model Inflation (TMI), Super-conformal Alpha Attractor B Inflation (SABI), Super-conformal Alpha Attractor T Inflation (SATI), Symmetry Breaking Kähler Inflation (SBKI), S-Dual Inflation (SDI), Smeared Higgs Inflation (SHI), Mukhanov Inflation (VFMI). The inclusion of these models allows the new edition to provide an up-to-date landscape of all single-field slow-roll inflationary models, bringing the number of models included in the ASPIC library to 118.
Second, at the observational level, the first edition compared the predictions of single-field models with the early release of the Planck 2013 data. Since then, additional data has been collected, and the second edition features second-order slow-roll constraints from the full Planck Legacy + Bicep-Keck data combination. The Bayesian evidence of all models has also been re-computed with the new data set, and the results will be presented in a separate publication.
Third, as the accuracy of the recent data releases has kept improving, several projects are on their way that should deliver even more accurate cosmological data in the years to come. In particular, let us mention ground-based experiments that are currently operating such as BICEP3 & Keck array and SPT in Antarctica, QUIJOTE in the Canary islands, and CLASS, ACT and Polarbear in the Atacama desert. They have been very recently joined by QUBIC. In space, the Euclid satellite is soon to be launched and will provide unprecedented measurements on the matter power spectrum, down to very small scales. The LiteBIRD satellite is planned to be launched in 2028 and should allow us to further constrain the \(B\)-mode signal in the polarisation of the CMB. These prospects of ever increasing precision confirm the relevance of the original Encyclopædia Inflationaris and ASPIC projects, namely the need for accurate predictions on a model-to-model basis. For this reason, we have continued to pay special attention to solve the inflationary dynamics exactly, without any other approximations than those contained in the slow-roll framework. This one has indeed been shown to be sufficiently accurate for the Planck CMB data [8] and can be extended to arbitrary precision if needed [9]. On the contrary, as discussed in Ref. [10] other commonly-employed approximations are now too imprecise to allow for a fair comparison with the data.
Some of the new models are compatible with the present data, as one could have expected, but this statement is strongly reheating dependent. This can be illustrated by the following figure. It shows their predictions, namely spectral index \(n_\mathrm{S}\) and tensor-to-scalar ratio \(r\) as a function of the reheating energy scale \(E_{\mathrm{reh}}\) (assuming a matter-like reheating for illustration purposes). The contours are the \(68\%\) and \(95\%\) confidence intervals associated with the successive Planck data releases since 2013.
As this figure shows, getting reheating-consistent predictions has never been so crucial. The reheating expansion history determines the part of the inflationary potential being probed by cosmological measurements, it can now substantially affect the preference shown by the data for a given model (in technical terms, the Bayesian evidence). This is one of the reasons why, in the opirarous edition, the Starobinsky model (SI) and Higgs Inflation (HI) are now treated as distinct models, since they come with different reheating histories. Moreover, even though they are often treated as sharing the same potential, this is only correct at leading order in an expansion with respect to the inverse of the non-minimal coupling of the field. Differences arise at next-to-leading order that we now account for in an exact manner.
The previous figure certainly confirms the strategy adopted since the early days of Encyclopædia Inflationaris to derive reheating-consistent predictions. Ignoring it can indeed be catastrophic. As an example, here are the reheating-consistent predictions of one of the new model proposed after the Planck data release. Not including reheating effects would imply selecting random points in this mess…
Let us note that in its new edition, the format of the paper has been purposely kept similar to its original version. In particular, the introduction (section 2) has been essentially left untouched in order to keep track of our original motivations, and of the main considerations that were discussed in the field at that time. We have also not completed section 3 with a list of new analytical results derived in the 46 new potentials, given that we think it has already become clear that Encyclopædia Inflationaris is more than a review indeed. At the time of this post, the opiparous edition is made public only through arXiv:1303.3787v4 with a full open access CC BY-NC-SA 4.0 license.
Finally, about the benefit of a second edition, let us quote Jean Le Rond d’Alembert (in a letter to Voltaire, June 23, 1766):
Quant à l’ouvrage, il est maigre, mais il est aisé de lui donner de l’embonpoint dans une seconde édition.
These models may nonetheless come with different values for the parameters describing the potential, i.e. different priors in the framework of a Bayesian analysis. ↩
At 2pm, room E349, Danièle Steer (APC), will be talking about
In this talk I will outline the main different methods on the market for measuring cosmological parameters (including modified gravity parameters) with GWs, and the main sources of errors in these measurements. Then I will highlight the current results on cosmological parameters obtained with the O3 run of LIGO-Virgo, as well as give predictions for future expectations. Finally I will go into more technical details and explain an analytical approach to estimate distance errors with GW observations (from any number of ground based interferometers placed at different positions on earth).
]]>The live stream can be watched there while a transcripted english translation has been published on the arXiv.
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