Chapter 1
Introduction and Summary
In the last few decades several impressive observational achievements (see e.g. [1–
4]) allowed the development of a “concordance” model of cosmology, the so-called
“CDM” model, whose parameters are now determined with below percent accuracy. Remarkably, the physics involved in this model is mostly conservative, as it
essentially relies on the theory of General Relativity (GR) and the Standard Model
(SM) of particle physics. Both of them are mature modelizations of nature, in that
they have been tested extensively and in various contexts for several decades, if not
a century. Nevertheless, there are also important “black boxes” in this construction,
the most prominent ones arguably being the dark energy and dark matter components of the universe (or effects).
1 Understanding this dark sector is one of the most
profound challenges of modern physics, with several future surveys being devoted
to this task, be it fully or partially [5–9]. These advances will increase the precision
that is required from the theoretical predictions in order to correctly interpreted the
data. The case of particular interest in this work is the definition and computation of
cosmological observables, i.e. the reconstruction of the physical quantities measured
by the observer out of the information on the latter’s light-cone. The linear order perturbation theory around the homogeneous and isotropic solution is well understood
and documented, but is often insufficient for matching the aforementioned precision
requirements. This is why, in the last decade, the community has been actively investigating the impact of second-order effects in the CMB lensing [10–21], in galaxy
number counts [22–36] and cosmological distances and weak lensing [37–45].
Despite this important literature on the subject, it turns out that the approaches
employed so far contain an approximation that is no longer justified at non-linear
orders, thus potentially invalidating several results. This is a bold claim, so it is
worth laying down some supporting material in order to make our point. First, we
1 Other important open questions include the physics of inflation and the generation of baryon
asymmetry in the early universe, or the microscopic physics behind the neutrino mass.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
E. Mitsou and J. Yoo, Tetrad Formalism for Exact Cosmological Observables,
SpringerBriefs in Physics, https://doi.org/10.1007/978-3-030-50039-9_1
1
Introduction and Summary
In the last few decades several impressive observational achievements (see e.g. [1–
4]) allowed the development of a “concordance” model of cosmology, the so-called
“CDM” model, whose parameters are now determined with below percent accuracy. Remarkably, the physics involved in this model is mostly conservative, as it
essentially relies on the theory of General Relativity (GR) and the Standard Model
(SM) of particle physics. Both of them are mature modelizations of nature, in that
they have been tested extensively and in various contexts for several decades, if not
a century. Nevertheless, there are also important “black boxes” in this construction,
the most prominent ones arguably being the dark energy and dark matter components of the universe (or effects).
1 Understanding this dark sector is one of the most
profound challenges of modern physics, with several future surveys being devoted
to this task, be it fully or partially [5–9]. These advances will increase the precision
that is required from the theoretical predictions in order to correctly interpreted the
data. The case of particular interest in this work is the definition and computation of
cosmological observables, i.e. the reconstruction of the physical quantities measured
by the observer out of the information on the latter’s light-cone. The linear order perturbation theory around the homogeneous and isotropic solution is well understood
and documented, but is often insufficient for matching the aforementioned precision
requirements. This is why, in the last decade, the community has been actively investigating the impact of second-order effects in the CMB lensing [10–21], in galaxy
number counts [22–36] and cosmological distances and weak lensing [37–45].
Despite this important literature on the subject, it turns out that the approaches
employed so far contain an approximation that is no longer justified at non-linear
orders, thus potentially invalidating several results. This is a bold claim, so it is
worth laying down some supporting material in order to make our point. First, we
1 Other important open questions include the physics of inflation and the generation of baryon
asymmetry in the early universe, or the microscopic physics behind the neutrino mass.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
E. Mitsou and J. Yoo, Tetrad Formalism for Exact Cosmological Observables,
SpringerBriefs in Physics, https://doi.org/10.1007/978-3-030-50039-9_1
1