# Primordial anisotropies

In the context of the Voyage 2050 mission, we plan to perform a nearly cosmic-variance-limited measurement of the **CMB temperature and polarization anisotropies**** **in a much wider range of angular scales than the Planck satellite. The power spectrum (or two-point correlation function) expected from the Voyage 2050 maps will be ideal to constrain, among others, **cosmic inflation** and the properties of **neutrinos** (or neutrino-like particles).

**Cosmic inflation** is the most elegant solution to explain the degree of flatness and of homogeneity of our Universe, as well as the generation of two types of primordial perturbations from quantum fluctuations: density perturbations, which are called scalar perturbations, and primordial gravitational waves, called tensor perturbations. While past observations have brought many indirect evidencer in favour of this stage of early accelerated cosmological expansion, several aspects of inflation remain unconstrained. The Voyage 2050 mission will allow us to better understand inflation by probing:

**Primordial g****ravitational waves.**CMB B-mode polarization offers a unique window for detecting gravitational waves from inflation at an energy scale approximately a trillion times higher than those probed by the Large Hadron Collider. Our ambitious goal is to be sensitive to a tensor-to-scalar ratio in the primordial fluctuations of the order of r ∼ 10−4, approximately 300 times better than the current sensitivity [1,2], and one order of magnitude below the uncertainty targeted by any single CMB experiment in the next decade. Classes of inflationary models motivated by string theory or supergravity, predicting r ~ 10−3, could be probed unambiguously. As an example, the Kahler geometry of α- attractor models motivated by maximal supersymmetry [3,4] could be probed entirely at high statistical significance. In the case of no detection, a vast class of large-field inflationary models will be ruled out.**The spectrum of primordial density perturbations.**The mission is expected to measure the power spectrum of curvature perturbations on a wide range of angular scales and with a precision that are unprecedented for a single experiment. It will measure the scalar spectral index ns with an accuracy of ~0.0015, which is more than a factor of three tighter than current measurements. It will also constrain the running of the spectral index with a similar error bar of ~0.0015, at the same level as the theoretical predictions for single-field slow-roll inflationary models that provide a best-fit to Planck data, such as R2 or Higgs inflation. The proposed survey will therefore have the capability to discriminate among different inflationary models also on the basis of the second derivative of the power spectrum.**Primordial non-gaussianity.**Standard single-field slow-roll inflationary models predict primordial fluctuations with highly Gaussian statistics, compatible with the most recent Planck constraints on the local, equilateral, and orthogonal shapes of the bispectrum [5]. We can improve by a factor 2–3 on these bispectrum constraints, which are important to constrain models beyond the simplest ones, such as those with a non-trivial sound speed for the inflaton or with multiple fields. An enhanced sensitivity to the local shape of the bispectrum down to f_local ∼ 1, which is an important threshold for multi-field inflationary models, can also be reached by a tomographic cross-correlation of the lensing potential measured by the Voyage 2050 mission with deep radio or photometric surveys in preparation, such as EMU, SKA or LSST.

The evolution of our universe depends on the type and the properties of the particles that it contains. We know that beyond ordinary matter, dark matter and photons, our universe contains at least **neutrinos** with a non-zero but yet unknown mass, and possibly other similar **light or massless relic particles** belonging to an extension of the standard model of particle physics. The data from the proposed Voyage 2050 mission will provide crucial information on:

**The summed mass of ordinary neutrinos.**Inferring the neutrino mass sum Mν from cosmological data will remain a crucial target in the long term, since planned laboratory experiments are not sensitive to the minimal value Mν = 0.06eV. Besides, it is important to exploit the synergy between cosmological surveys and laboratory searches, which are sensitive to different neutrino-related parameters and assumptions. On the cosmology side, precise measurements of Mν require an exquisite mapping of both CMB anisotropies and large-scale structures (LSS). The two categories of observables are directly sensitive to the reduction in the growth rate of matter fluctuations induced by Mν, which CMB surveys probe through CMB lensing. CMB surveys will also play an essential role in accurately measuring other parameters like τ, ns, H0, and ωc, that reduce degeneracies with Mν in the analysis of LSS data. The Voyage 2050 mission alone is expected to reach a sensitivity of Mν ~ 0.04 eV, and will be crucial in order to detect Mν up to a ~0.01eV uncertainity in combination with future galaxy, cosmic shear, and intensity-mapping surveys.A plethora of extensions of the standard model of particle physics predict a relic density of extra light particles that would show up as an increase in the

**effective neutrino number**Neff beyond its standard value of 3.045 [6]. Measuring Neff is thus crucial for particle physics. CMB anisotropies are the most sensitive probe of Neff. Voyage 2050 will provide unprecedented sensitivity to Neff, reaching an error bar of ~0.022 using temperature and polarization, and down to ~0.016 in combination with CMB lensing extraction. In absence of extra relics, the standard value 3.045 will be distinguished from 3.0 at the 2–3σ level, which will offer an accurate test of the standard model of neutrino decoupling and electron-positron annihilation. The possibility that any new scalar boson decouples from the standard model at some temperature T < 103 TeV will be either established or excluded at the 1.5σ level (2σ or 3σ for a fermion or vector boson, respectively). A measurement compatible with 3.046 would prove with the same significance that no new particles have left thermal equilibrium between the decoupling of top quarks (at redshift z ∼ 1014) and today.Voyage 2050 will also be very sensitive to additional effects caused by the small mass of possible light non-thermal

**sterile neutrinos**(whose effect would be roughly equivalent to a combination of Mν and Neff ), or to**non-standard interactions in the neutrino sector**(that would modify the so-called neutrino drag effects, particularly visible on intermediate and small scales in the polarization spectrum).

[1] P. A. R. Ade et al. (BICEP2, Keck Array), Phys. Rev. Lett. 121, 221301 (2018), 1810.05216.

[2] Planck Collaboration 2018 X (Planck) (2018), 1807.06211.

[3] S. Ferrara and R. Kallosh, Phys. Rev. D 94, 126015 (2016), 1610.04163.

[4] R. Kallosh, A. Linde, T. Wrase, and Y. Yamada, Journal of High Energy Physics 2017, 144 (2017), 1704.04829.

[5] Planck Collaboration 2018 IX (Planck) (2019), 1905.05697.

[6] P. F. de Salas and S. Pastor, JCAP 2016, 051 (2016), 1606.06986.