Tests of Special Relativity and Gravity
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Questions and Answers

What condition must be satisfied for the scalar curvature to be constant in the given equation?

  • The mass of the universe must be zero.
  • The density of the universe must be negative.
  • The radiation must dominate. (correct)
  • The energy-momentum tensor must be non-conserved.

    • What does equation (5.3.16) indicate about the state of the universe?

  • The universe is contracting.
  • The universe is expanding. (correct)
  • The universe is static.
  • The universe is collapsing into a singularity.

    • What occurs if the parameter k vanishes within the context of the universe?

  • The universe cannot exist.
  • The universe is in a state of infinite density.
  • There are no atoms to exert pressure. (correct)
  • The universe undergoes rapid expansion.

    • What implication arises when k is positive as discussed in the content?

    <p>Imaginary quantities begin to dominate.</p> Signup and view all the answers

    What does the new equation explore regarding scalar curvature?

    <p>It allows fluctuation in scalar curvature over time.</p> Signup and view all the answers

    What is indicated by the cosmological constant problems?

    <p>There is a disparity between present small and early large vacuum energy.</p> Signup and view all the answers

    What does the singularity problem in cosmology refer to?

    <p>The density of the universe is infinite at initial conditions.</p> Signup and view all the answers

    What does the horizon problem in cosmology identify?

    <p>The universe has different temperatures and densities in its early state.</p> Signup and view all the answers

    What aspect is related to the flatness problem in cosmology?

    <p>The relation between the universe density and critical density at plank time.</p> Signup and view all the answers

    Which statement about vacuum energy at different times is correct?

    <p>Large vacuum energy can cause cosmic inflation.</p> Signup and view all the answers

    What is a consequence of finite physical quantities in cosmology?

    <p>Realistic models require finite densities.</p> Signup and view all the answers

    How does the early universe's structure relate to the horizon problem?

    <p>Different regions implied isolation and non-uniformity.</p> Signup and view all the answers

    What is the significance of the cosmic scale factor being zero?

    <p>It indicates a starting point of infinite density.</p> Signup and view all the answers

    What is the primary difference between gravitational equations and Maxwell's equations?

    <p>Gravity influences its source, while electric charge is not affected by its field.</p> Signup and view all the answers

    What is one suggested basis to improve general relativity theory?

    <p>Inclusion of a quadratic term in the Lagrangians.</p> Signup and view all the answers

    What is required for the scalar curvature in the equation of motion solutions?

    <p>It must be constant.</p> Signup and view all the answers

    What drives inflation according to the discussed equations?

    <p>A repulsive force.</p> Signup and view all the answers

    What must the term reflecting matter or vacuum density be for inflation to occur?

    <p>Positive.</p> Signup and view all the answers

    Which equation indicates a dominance of quadratic over linear terms during inflation?

    <p>Equation (5.2.22).</p> Signup and view all the answers

    For the inflation solution to hold true, how should the scalar curvature be treated?

    <p>As a large constant value.</p> Signup and view all the answers

    According to the inflation model, what signifies the possibility of inflation taking place?

    <p>A positive sign in specified equations.</p> Signup and view all the answers

    What does the quantity ǫ represent in the context of gravity?

    <p>A measure distinguishing strong from weak gravity</p> Signup and view all the answers

    Which experiment is primarily associated with testing the equivalence principle?

    <p>Gravity Probe-B</p> Signup and view all the answers

    In which scenario is the value of ǫ approximately 0.5?

    <p>Near the event horizon of a black hole</p> Signup and view all the answers

    What significant phenomenon does the big bang represent in cosmology?

    <p>The initial singularity marking the beginning of the universe</p> Signup and view all the answers

    What are the strong gravitational fields associated with Planck-scale physics known for?

    <p>Leaving observable effects accessible by experiment</p> Signup and view all the answers

    What does ongoing research aim to explore regarding black holes and neutron stars?

    <p>The dynamics and strong-field regime of general relativity</p> Signup and view all the answers

    Which aspect of gravity is being tested through experiments of large extra dimensions?

    <p>The inverse square law of gravity</p> Signup and view all the answers

    What is a common characteristic of the regime of weak gravity?

    <p>ǫ is less than $10^{-5}$</p> Signup and view all the answers

    What happens to the universe's energy density as it expands?

    <p>It decreases.</p> Signup and view all the answers

    In the context provided, what is assumed to stand for vacuum energy?

    <p>A constant term.</p> Signup and view all the answers

    What occurs when the curvature parameter is positive?

    <p>The universe expands with vanishing scalar curvature.</p> Signup and view all the answers

    Which equation gives a possible solution to the behavior of the universe?

    <p>(5.4.14)</p> Signup and view all the answers

    What does the first term in the universe density expression indicate?

    <p>Density decreases as the universe expands.</p> Signup and view all the answers

    What is indicated when the radius parameter in equation (5.4.1) changes?

    <p>Contraction of the universe.</p> Signup and view all the answers

    What confirms models where quantum mechanical laws describe the early universe?

    <p>The use of complex operators and wave functions.</p> Signup and view all the answers

    What is required for c to be real in the equations mentioned?

    <p>Specific solutions in the equations must hold.</p> Signup and view all the answers

    Study Notes

    The Cosmological Constant Problems

    • The cosmological constant in General Relativity (GR) represents vacuum energy.
    • Observations show that vacuum energy is currently negligible, contrasting with its high values in the early universe leading to inflation.
    • The disparity between small present and large early vacuum energy is referred to as the cosmological constant problem.

    The Singularity Problem

    • The Standard Big Bang (SBB) model posits that the universe began at an initial singularity with infinite density.
    • Such infinite density is not physically acceptable, leading to what is known as the singularity problem.

    The Horizon Problem

    • The horizon problem arises from the light sphere radius being much smaller than the radius of the universe.
    • Early universe light spheres were isolated due to light speed limits, causing different temperatures and densities, contradicting observations of a homogeneous universe.
    • This lack of interaction among isolated light spheres leads to the horizon problem.

    The Flatness Problem

    • The flatness problem relates the critical density and actual density of the universe.
    • A slight initial deviation from critical density could lead to a universe that is either collapsing or expanding, causing stability issues.

    Break Down of GR in Cosmology

    • The big bang linked to the singularity represents a breakdown in GR's applicability, showing limitations in resolving initial singularities.
    • The nonlinear nature of gravitational equations contrasts with the linearity of Maxwell’s equations governing electromagnetism.

    Solutions with Constant Scalar Curvature

    • Constant scalar curvature solutions imply that the scalar curvature remains constant throughout, leading to simplified models of inflation.
    • Specific equations indicate how inflation can lead to an expanding universe consistent with astronomical observations.
    • The expansion is understood within a framework where vacuum density plays a critical role.

    Dynamical Scalar Curvature for Non-Singular Expanding Universe

    • The new equations allow for solutions describing time-varying scalar curvature, applying to both vacuum and radiation eras.
    • Several scenarios demonstrate how the universe can expand with a vanishing scalar curvature, confirming quantum mechanical behaviors in the early universe.
    • Notably, density expressions consist of terms indicating decreasing density with expansion, aligning with observational data and accounting for vacuum energy.

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