Unveiling the Dynamics of the Universe
Abstract
:1. Introduction
2. Scalar-tensor Theories
2.1. General Formalism
2.2. Conformal Picture
2.3. Cosmological Dynamics
- . This case corresponds to de Sitter solutions, dominated by the scalar field, and arise at non-vanishing maxima or minima of the potential V. Notice that may be different from 0. These solutions are attractors at minima of V and repellors at maxima of V.
- . The second case corresponds to matter dominated solutions with at maxima or minima of m. Note however that the system (15)–(18) is singular when , translating the fact that the variables in use are not regular. In the original variables, this second class of solutions exists provided that V has also an extremum, or is identically zero.
- , which lies on the invariant line , provided . These solutions (BM) correspond to those found in [114].
- , that lies in the interior of the phase space domain, provided that
2.4. Assisted Quintessence
2.4.1. General Equations
2.4.2. Scalar Field Dominated Solution
2.4.3. Scaling Solution
2.4.4. Scalar Potential Independent Solutions
- First, we have the kinetic dominated solutions where all the energy density for the dark sector is due to the kinetic energy of the scalar fields. In this instance, we have .
- As a second possibility, we have a contribution from the kinetic energy and the matter energy densities for the dark sector. In this case we have . This will be true for any matter species α since the sum is constrained to yield the same for all matter species.
- Finally, as a third possibility we have a matter dominated scenario. This has been investigated previously in the literature for the case of a single field with two matter components [128,130,131,132]. If we extend this to more than one field, we will see that there is a consistency condition imposed on the values of the couplings to allow a flat direction in the field space, otherwise this solution will be non existent. This is by its nature a transient solution since the matter contribution will eventually decay away and the scaling solution or the scalar field dominated solution will take over. However, this can be an interesting scenario for model building since it allows the dark matter sector to have a significant contribution before the acceleration of the Universe.
3. Horndeski Theories and Self-tuning
3.1. Dynamical Screening
- The field equation evaluated at the critical point has to be trivially satisfied leading the value of the field free to screen. This implies that the minisuperspace Lagrangian density at the critical point takes the form
- The full scalar equation of motion must depend on to allow for a non-trivial cosmological dynamics before screening. This leads to a condition equivalent to (45) if .
3.2. Requiring the Existence of a de Sitter Critical Point:
3.2.1. Linear Terms: “The Magnificent Seven”
3.2.2. Non-linear Terms
3.3. Cosmology of the Models
3.3.1. Example of a Linear Model
3.3.2. Example of a Non-Linear Model
3.4. Summary
4. Modified Theories of Gravity and Extensions
4.1. Modified Theories of Gravity
4.1.1. General Formalism
4.1.2. Discriminating between Dark Energy and Modified Gravity Models
4.1.3. Late-Time Cosmic Acceleration
4.2. Curvature-Matter Couplings in Gravity
4.3. The Palatini Approach
4.3.1. Quadratic Cosmology from Gravity-matter Coupling
4.3.2. Bouncing Cosmologies in Born-Infeld-like Gravity Models
4.4. Hybrid Metric-Palatini Gravity
4.4.1. General Formalism
4.4.2. Unifying Local Tests and the Late-Time Cosmic Acceleration
4.4.3. Future Outlook: More gEneral Hybrid Metric-Palatini Theories
4.5. Slow-Roll Inflation in Gravity
4.5.1. Inflationary Parameters
4.5.2. Inflation in Gravity
5. Topological Defects
5.1. Spontaneous Symmetry Breaking and Topological Defects
5.2. A VOS Model for Topological Defect Networks of Arbitrary Dimensionality
5.3. Observational Signatures of Topological Defects
5.3.1. CMB Anisotropies
5.3.2. The Stochastic Gravitational Wave Background
6. Cosmological Tests with Galaxy Clusters at CMB Frequencies
6.1. Galaxy Clusters
6.2. The SZ Effect: Temperature and Polarization Signal
6.3. Cosmological Tests Using SZ Cluster Surveys
6.3.1. SZ Cluster Counts
6.3.2. SZ Power Spectra
6.3.3. Probing New Physics with the SZ Clusters
6.4. Probing Primordial Non-Gaussianities with Galaxy Clusters
6.4.1. Parametrizing Primordial Non-Gaussianity
6.4.2. The Non-Gaussian Mass Function
6.4.3. Biased Cosmological Parameter Estimation with Cluster Counts
6.4.4. The Impact of pRimordial Non-Gaussianities on Galaxy Clusters Scaling Relations
7. Testing Gravity with Weak Lensing
7.1. Gravitational Lensing
7.2. Cosmic Shear
7.3. Testing Deviations from General Relativity
7.4. Testing Gravity with Future Cosmic Shear Data
8. Angular Distribution of Cosmological Parameters as a Measurement of Spacetime Inhomogeneities
8.1. Method of Local Parameter Estimation
8.2. Average over the Local Parameter Estimation
9. Summary and Conclusion
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Avelino, P.; Barreiro, T.; Carvalho, C.S.; Da Silva, A.; Lobo, F.S.N.; Martín-Moruno, P.; Mimoso, J.P.; Nunes, N.J.; Rubiera-García, D.; Sáez-Gómez, D.; et al. Unveiling the Dynamics of the Universe. Symmetry 2016, 8, 70. https://doi.org/10.3390/sym8080070
Avelino P, Barreiro T, Carvalho CS, Da Silva A, Lobo FSN, Martín-Moruno P, Mimoso JP, Nunes NJ, Rubiera-García D, Sáez-Gómez D, et al. Unveiling the Dynamics of the Universe. Symmetry. 2016; 8(8):70. https://doi.org/10.3390/sym8080070
Chicago/Turabian StyleAvelino, Pedro, Tiago Barreiro, C. Sofia Carvalho, Antonio Da Silva, Francisco S.N. Lobo, Prado Martín-Moruno, José Pedro Mimoso, Nelson J. Nunes, Diego Rubiera-García, Diego Sáez-Gómez, and et al. 2016. "Unveiling the Dynamics of the Universe" Symmetry 8, no. 8: 70. https://doi.org/10.3390/sym8080070