Theoretical cosmology
Goal: Understand the mathematical models of modern cosmology and their physics applications. Physical cosmology relates to a few other fields of science, such as astrophysics, astroparticle physics (a.k.a. particle astrophysics) and astronomy. Modern cosmology is grounded in general relativity and closely connected to quantum field theory on curved spacetime.
Group leader: Paul Tudorache
Group members: Paul Tudorache
Supervisors: Calin Lazaroiu and Mirela Babalic
Online resources for observational and computational aspects:
Some regional links
Latest estimates of cosmological parameters from the Particle Data Group.
The CMB temperature chart from WMAP.
A summary of the history of the universe.
Upcoming: Athena | SKAO | RST | LISA | Proposed space observatories | Gravitational wave observatories | PTAs | IPTA
Multimessenger astronomy and astrophysics
The Space Science website of the ESA
De Angelis, Cosmic Rays: multimessenger astrophysics and revolutionary astronomy, Springer, 2023.
Bindi et al, Cosmic ray physics
Schlickeiser, Cosmic ray astrophysics
Arguelles et al, From the Dawn of Neutrino Astronomy to A New View of the Extreme Universe, arXiv:2405.17623 [hep-ex]
Bailes et al, Gravitational-wave physics and astronomy in the 2020s and 2030s, Nature Reviews Physics 3 (2021) 344-366.
Flanaghan and Hughes, The basics of gravitational wave theory, New. J. Phys 7 (2005) 204.
Bambi et al, Handbook of gravitational wave astronomy
Maggiore, Gravitational waves, vols 1 & 2
Caprini, Strong evidence for the discovery of a gravitational wave background, Nature Reviews Physics 6 (2024) 291-293.
Scheme:
I. Basic cosmology
A. Cosmological solutions
B. FLRW spacetimes and equations of state
C. The basic history of the universe
D. Problems of early universe cosmology
E. Basic theory of one-field cosmological models
F. Special subjects
Bonus: Historical note.
References:
Introductory
Ryden, Introduction to Cosmology
Durrer, The cosmic microwave background
Intermediate to advanced
Ellis, Maartens and MacCallum, Relativistic cosmology
Dodelson and Schmidt, Modern cosmology
Weinberg, Cosmology
Weinberg, Gravitation and cosmology
Special subjects
Dynamical systems approach
Wainwright and Ellis, Dynamical Systems in Cosmology
Luminet, The wraparound universe.
Weeks, The shape of space.
COMPACT collaboration, Promise of Future Searches for Cosmic Topology, Phys. Rev. Lett. 132 (2024) 171501.
P. M. Vaudrevage et al, Constraints on the topology of the Universe: Extension to general geometries, Phys. Rev. D 86 (2012) 083526.
M. Lachieze-Rey, J. P. Luminet, Cosmic topology, Phys. Rep. 254 (1995) 135-214.
Dark matter:
Cirelli et. al, Dark Matter, arXiv:2406.01705 [hep-ph]
Structure formation
Primack, Galaxy Formation in ΛCDM Cosmology, Annu. Rev. Nucl. Part. Sci. 2024. 74 (2024) 173-206.
Primordial black holes
Arbey, Primordial black holes: a small review, arXiv:2405.08624 [gr-qc].
Escriva et al, Primordial black holes, in Sedda et al (eds), Black Holes in the Era of Gravitational-Wave Astronomy, Elsevier, 2024, pp. 261-377.
Green, Primordial black holes as a dark matter candidate - a brief overview, Nucl. Phys. B 1003 (2024) 116494.
History
Kragh, Conceptions of the cosmos
Kragh and Longair, The Oxford Handbook of the History of Modern Cosmology
II. Single-field early universe cosmology
A. The ADM formalism
B. Single field cosmological perturbation theory
C. The slow roll and psi-expansions of single-field models
D. Dynamical systems methods and attractors in single-field models
E. Reheating
F. Stochastic inflation
References:
A. The ADM formalism
Giulini, Dynamical and Hamiltonian formulation of general relativity, in Springer Handbook of Spacetime, Springer, 2014.
Corichi and Nunez, Introduction to the ADM formalism, Rev. Mex. Fis. 37 (1991) 4, 720-747.
Arnowitt, Deser and Misner, The dynamics of general relativity (republication of the 1962 classic paper).
Bojowald, Canonical gravity and applications
Ringstrom, The Cauchy problem in general relativity
CQG, WDW equation, "Quantum cosmology" and the Hartle-Hawking "no bounday" proposal
Cianfrani et al, Canonical Quantum Gravity
Kiefer, Quantum gravity
Bojowald, Foundations of quantum cosmology
B. Single field cosmological perturbation theory
Mukhanov, Physical foundations of cosmology
Brandenberger, Lectures on the theory of cosmological perturbations, Lect. Notes in Physics 646 (2004) 127-167.
Mukhanov, Feldman, Brandenberger, Theory of Cosmological Perturbations, Phys Rep. vols 215 & 216.
Bardeen, Gauge-invariant cosmological perturbations, Phys. Rev. D 22 (1980) 1882.
Salopek, Bond and Bardeen, Designing density fluctuation spectra in inflation, Phys. Rev. D 40 (1989) 1753.
Bardeen, Cosmological perturbations from quantum fluctuations to large scale structure (conference proceedings, 1988).
Ma and Bertschinger, Cosmological Perturbation Theory in the Synchronous and Conformal Newtonian Gauges, Astrophys. J. 455 (1995) 7.
Uggla and Wainwright, Cosmological perturbation theory revisited, Class Quantum Grav, 28 (2011) 175017.
Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models, JHEP 0305 (2003) 013.
C. The slow roll and psi-expansions of single-field models
Liddle, Parsons, Barrow, Formalizing the slow-roll approximation in inflation, Phys. Rev. D 50 (1994) 7222.
C. I. Lazaroiu, On the slow roll expansion of one-field cosmological models, Nucl. Phys. B 1000 (2024) 116466.
E. Medina, L. M. Alonso, Kinetic dominance and psi series in the Hamilton-Jacobi formulation of inflaton models, Phys. Rev. D 102 (2020) 103517.
W. Handley, A. Lasenby, M. Hobson, Logolinear series expansions with applications to primordial cosmology, Phys. Rev. D 99 (2019) 123512.
W. Handley, A. Lasenby, M. Hobson, Logolinear series expansions with applications to primordial cosmology, Phys. Rev. D 99 (2019) 123512.
D. Dynamical systems methods and attractors in single-field models
Rendall, Cosmological models and center manifold theory, Gen. Rel. Grav. 34 (2002) 1277.
Rendall, Late-time oscillatory behaviour for self-gravitating scalar fields, Class. Quant. Grav. 24 (2007) 667.
Ahlo and Uggla, Global dynamics and inflationary center manifold and slow-roll approximants, J. Math. Phys. 56 (2015) 012502.
Ahlo, Hell, Uggla, Global dynamics and asymptotics for monomial scalar field potentials and perfect fluids, Class Quantum Grav. 32 (2015) 145005.
Ahlo and Uggla, Inflationary α-attractor cosmology: A global dynamical systems perspective, Phys. Rev. D 95 (2017) 083517.
Alvarez, Alonso, Medina & Vazquez, Separatrices in the Hamilton-Jacobi Formalism of Inflaton Models, J. Math. Phys. 61 (2020) 043501.
E. Reheating
Lozanov, Reheating after inflation
K. Lozanov, Lectures on reheating after inflation
F. Stochastic inflation
Launay et al, Stochastic inflation in general relativity, Phys. Rev. D 109 (2024) 123523.
Pattison et al, Stochastic inflation beyond slow roll, JCAP 07 (2019) 031.
III. Two-field and multifield early universe cosmology
A. Basic theory. Kinematic and dynamical parameters
B. Formulation as geometric dynamical systems. Cosmological observables
C. The SRST and SRRT conditions
D. SRST inflation
E. Rapid turn inflation
F. Noether symmetries
G. Multifield cosmological perturbation theory
H. Reheating in multifield models
K. Stochastic inflation in multifield models
L. Constraining multifield inflation using observational data
References:
A. Basic theory. Kinematic and dynamical parameters
A. Hetz, G.A. Palma, Sound Speed of Primordial Fluctuations in Supergravity Inflation, Phys. Rev. Lett. 117 (2016) 101301.
B. Formulation as geometric dynamical systems. Cosmological observables
C. I. Lazaroiu, Dynamical renormalization and universality in classical multifield cosmological models, Nucl. Phys. B 983 (2022) 115940.
E. M. Babalic, C. I. Lazaroiu, The infrared behavior of tame two-field cosmological models, Nucl. Phys. B 983 (2022) 115929.
C. I. Lazaroiu, Natural observables and dynamical approximations in multifield cosmological models, Int. J. Mod. Phys. A. 38 (2023) 32, 2343007.
C. The SRST and SRRT conditions
C. M. Peterson, M. Tegmark, Testing Two-Field Inflation, Phys. Rev. D 83 (2011) 023522.
L. Anguelova, C. I. Lazaroiu, Dynamical consistency conditions for rapid turn inflation, JCAP 05 (2023) 020.
D. SRST inflation
C. M. Peterson, M. Tegmark, Testing Two-Field Inflation, Phys. Rev. D 83 (2011) 023522.
C. M. Peterson, M. Tegmark, Non-Gaussianity in Two-Field Inflation, Phys. Rev. D 84 (2011) 023520.
E. Rapid turn inflation
General features
S. Reneaux-Petel, Inflation with strongly non-geodesic motion: theoretical
motivations and observational imprints, EPS proceedings (EPS-HEP2021).
motivations and observational imprints, EPS proceedings (EPS-HEP2021).
R. Z. Ferreira, Non-Gaussianities in models of inflation with large and negative entropic masses, JCAP 08 (2020) 034.
D.-G. Wang. G. L. Pimentel, A. Achucarro, Bootstrapping Multi-Field Inflation: non-Gaussianities from light scalars revisited, JCAP 05 (2023) 043.
O. Yaryghina, M.C.D. Marsh, G. Salinas, Non-Gaussianity in rapid-turn multi-field inflation, JCAP 03 (2024) 014.
Models
A. Brown, Hyperinflation, Phys. Rev. Lett. 121 (2018) 251601.
S. Mizuno, S. Mukohyama, Primordial perturbations from inflation with a hyperbolic field space, Phys. Rev. D 96 (2017) 103533.
T. Bjorkmo, M. C. D. Marsh, Hyperinflation generalised: from its attractor mechanism to its tension with the ‘swampland conditions’, JHEP 04 (2019) 172.
S. Garcia-Saenz, S. Renaux-Petel, J. Ronayne, Primordial fluctuations and non-Gaussianities in sidetracked inflation, JCAP 1807 (2018) 057.
P. Christodoulidis, D. Roest, E. Sfakianakis, Angular inflation in multi-field α-attractors, JCAP 11 (2019) 002.
J. Ellis, M. Garcia, D. Nanopoulos, K. Olive, Two-Field Analysis of No-Scale Supergravity Inflation, JCAP 01 (2015) 010.
F. Noether symmetries
L. Anguelova, E. M. Babalic, C. I. Lazaroiu, Hidden symmetries of two-field cosmological models, JHEP 09 (2019) 007.
G. Multifield cosmological perturbation theory
C. M. Peterson, M. Tegmark, Non-Gaussianity in Two-Field Inflation, Phys. Rev. D 84 (2011) 023520.
In spatially flat gauge
J. Elliston, D. Seery, R. Tavakol, The inflationary bispectrum with curved field-space, JCAP 1211 (2012) 060.
D. Seery, J. E. Lidsey, Primordial non-gaussianities from multiple-field inflation, JCAP 0509 (2005) 011.
D. Langlois, S. Renaux-Petel, Perturbations in generalized multi-field inflation, JCAP 0804 (2008) 017.
D. Langlois, S. Renaux-Petel, D. A. Steer, T. Tanaka, Primordial perturbations and non-Gaussianities in DBI and general multifield inflation, Phys. Rev. D78 (2008) 063523.
E. Tzavara, B. van Trent, Gauge-invariant perturbations at second order in two-field inflation, JCAP 1208 (2012) 023.
E. Tzavara, S. Mizuno, B. van Tent, Covariant second-order perturbations in generalized two-field inflation, JCAP 1407 (2014) 027.
In "comoving" gauge
S. Garcia-Saenz, L. Pinol and S. Renaux-Petel, Revisiting non-Gaussianity in multifield inflation with curved field space, JHEP01 (2020) 073.
L. Pinol, Multifield inflation beyond Nfield=2: non-Gaussianities and single-field effective theory, JCAP04 (2021) 002.
Structural
L. Pinol, S. Renaux-Petel, D. Werth, The Cosmological Flow: A Systematic Approach to Primordial Correlators, arXiv:2312.06559 [astro-ph.CO].
M. Braglia, L. Pinol, No time to derive: unraveling total time derivatives in in-in perturbation theory, JHEP 08 (2024) 068.
H. Reheating in multifield models
J. Martin, L. Pinol, Opening the reheating box in multifield inflation, JCAP 12 (2021) 022.
K. Stochastic inflation in multifield models
L. Pinol, S. Renaux-Petel, Y, Tada, A manifestly covariant theory of multifield stochastic inflation in phase space, JCAP04 (2021).
M. Honda, R. Jinno, L. Pinol, K. Tokeshi, Borel resummation of secular divergences in stochastic inflation, JHEP08 (2023) 060.
A. Achucarro, S. Cespedes, A.-C. Davis, G. A. Palma, The hand-made tail: non-perturbative tails from multifield inflation, JHEP05(2022)052.
L. Constraining multifield inflation using observational data
Giare et. al., Tracking the Multifield Dynamics with Cosmological Data: A Monte Carlo approach, JCAP12(2023)014.
Cabass et al, Constraints on multifield inflation from the BOSS galaxy survey, Phys. Rev. D 106 (2022) 043506.
Cecchini et al, Testing scale-invariant inflation against cosmological data, JCAP07 (2024) 058.