At 2pm, room E349, **Eemeli Tomberg** (Lancaster University), will be talking about

*Quantum fluctuations from cosmic inflation give rise to the
macroscopic structures of the universe. The strongest fluctuations
collapse into primordial black holes, a dark matter candidate and a
possible source of gravitational waves. Stochastic inflation is a
tool to compute the fluctuation statistics non-perturbatively, needed
for accurate black hole predictions. I discuss recent progress in
these computations, their numerical implementation and analytical
approximations, and the implications for black hole abundance in
single-field models of inflation.*

**Hopes of Big Bang Discoveries Ride on a Future Spacecraft**

More details can be found in the scientific paper Ref. [1] and this **post**.

Primordial black holes (PBH) are cosmological objects that could have been formed in the earliest instants of the universe’s history, for instance, when large overdensities collapse under their own gravity. Understanding how these PBHs cluster is essential as it can provide insights into the evolution of structure formation in the universe and could potentially help in assessing how much, and when, binaries of these objects appear.

In Ref. [1], **Pierre**
and **Baptiste** have used the excursion-set
formalism to quantify the initial spatial clustering of PBHs generated
from large Gaussian density fluctuations. Their method takes into
account the “cloud-in-cloud” mechanism, which is a critical aspect
that is overlooked in studies using the Poisson model of clustering.

In the excursion-set formalism, the collapse of an overdensity to form a PBH of mass \(M\) is recast into the probability of finding the first crossing of a random walk at some scale \(S(M)\). This approach has been already applied to study the formation of large-scale structure, in which multiple crossings of a random walk describe a hierarchy of structures. This formalism was first developed to solve the “cloud-in-cloud” problem, that is resolving this hierarchy of structures.

The cloud-in-cloud mechanism implies that PBHs should be part of larger structures: they don’t just appear randomly as per the Poisson assumption. This results in a natural and intrinsic correlation between the formation of pairs of PBHs, which is important for accurately modelling the clustering behaviour at small scales. The following picture shows two random walks that share a common past until the “time” \(S_{r}\): they come from the same realisation of a large scale density perturbation. Subsequently, they evolve in distinct ways and this results in two different collapses that occur respectively at the first-crossing times \(S_{1}\) and \(S_{2}\)

Such an approach automatically includes short-range exclusion effects: PBHs are anti-correlated at short distances!

The authors also present explicit expressions for the excess probability to find pairs of PBHs separated by a given distance and for the excess probability to find pairs with an asymmetric mass ratio.

]]>LISA will be the next-generation observatory in the field of
gravitational waves, surpassing current terrestrial capabilities by
exploring lower frequencies and longer timescales, opening up a new
observation window into the universe. and technological
innovation. The LISA definition study report, in which **Pierre** was a
contributor, presents an in-depth analysis of the mission’s scientific
rationale, design, and implementation plans, see Ref. [1]. It highlights the
groundbreaking discoveries that LISA is expected to make

With ESA’s approval, the LISA mission moves one step closer to reality!

]]>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.*