Consider the following line element, ds² = -dt² + a² (t) (dx² + dy²) + b² (t) dz², where a(t) and b(t) are distinct functions. State whether or not this line element obeys the Cosmological Principle, if applied to describe the universe on large scales. Justify your answer.
Q: An optical spectrum of a galaxy has a magnesium absorption line at a wavelength of 531.3 nm. Given…
A:
Q: Suppose the energy density of the cosmological constant is equal to the present critical density En…
A: Einstein came up with the universal or cosmological constant to balance the calculations in his…
Q: Please answer within 90 minutes.
A: a. b.
Q: Assume a flat Friedmann-Robertson-Walker universe, and that the density parameters for matter…
A:
Q: 0.145 kg and radius rh = 0.0369 m. If the baseballs ated uniformly throughout the universe, what…
A: Given: The mass of baseball is 0.145 kg. The radius is 0.0369 m. Let m be the mass of…
Q: Suppose a hypothetical universe is expanding (at some moment in time) at a rate of H. At this same…
A: Given that for a universe Rate of expanding H = 90 km s-1 Mpc-1 And at this time the density ρ =…
Q: cos have to do with it. But either way, I'm still stuck in the same place. I don't know how you…
A:
Q: Consider a universe identical to ours, but where the only difference is that the mass of the proton…
A: Here is the explanation in the given image
Q: The Klein-Gordon equation at background level for a scalar field φ is given by (found in image…
A: Required : Slow roll inflation condition
Q: Consider a universe identical to ours, but where the only difference is that the mass of the proton…
A: Mean life: It is the average lifetime of a neutron which can be calculated as:τ=1λ. Here τ is the…
Q: Estimate the non-relativistic degeneracy pressure at the center of a 1.4 Msun neutron star…
A: The mass of the neutron star is given as, M=1.4MSun The mass of sun is given as, MSun=1.989×1030 kg.…
Q: 2 Consider Einstein's static universe, in which the attractive force of the matter density p is…
A:
Q: If a galaxy is 9.3 Mpc away from Earth and recedes at 508 km/s, what is H, (in km/s/Mpc)? 54.62…
A:
Q: In a homogeneous and isotropic universe we can represent all distances s by a time- independent…
A:
Q: State expressions for the effective energy density of the curvature term, Pk and the energy density…
A:
Q: solved
A: Given that the sphere has a uniform polarization P=P0 hat z, we can write the electric polarization…
Q: Any two-dimensional metric satisfiesR_λρµν = R/2 (g_λµ g_ρν − g_λν g_ρµ).Show that the vacuum…
A: The objective of the question is to demonstrate that any two-dimensional metric satisfies the vacuum…
Q: Any two-dimensional metric satisfies R_λρµν = R/2 (g_λµ g_ρν − g_λν g_ρµ). Show that the vacuum…
A: Show that the vacuum Einstein equations (with zero cosmological constant) are satisfied for any2D…
Q: Consider the following hypothetical reaction, involving an unknown meson, X. The meson has zero…
A: Step 1: Step 2: Step 3: Step 4:
Q: I understand we need to start with: GPEA + KEA = Wf + GPEC + KEC mghA + 0 = umgL + mghC +…
A: The initial height of the object is point A is hA = 18 m The final height of the object is at the…
Q: 1. Assume a flat Friedmann-Robertson-Walker universe dominated by a cosmological constant. Calculate…
A: The Friedmann-Robertson-Walker metric is based on the accurate solution of Einstein's general…
Q: According to the version of the Big Bang Theory without a Cosmological Constant (and without Dark…
A: Hubble's Law states that as the universe is expanding in all directions, the receding velocity of an…
Q: Consider the following line element, ds^2 = −dt^2 + a^2(t) (dx^2 + dy^2) + b^2(t) dz^2, where a(t)…
A: The objective of the question is to determine whether the given line element obeys the Cosmological…
Q: The rest wavelength of the Hα transition of atomic hydrogen is 656.3 nm (recall that 1 nm=10-9 m).…
A:
Q: Assume a flat Friedmann-Robertson-Walker universe, and that the density parameters for matter,…
A:
Q: Please answer within 90 minutes.
A: c) Calculate the Critical Density of the Universe TodayUsing H0=68 km/s/Mpc: H0=2.20×10−18 s−1…
Q: Consider the following line element, ds^2 = −dt^2 + a^2 (t) (dx^2 + dy^2 ) + b^2 (t) dz^2 , where…
A: Required: State whether or not this line element obeys the Cosmological Principle, if applied to…
Q: Derive the Wein Displacement Law by setting the derivative of the following function equal to zero…
A: Introduction: The magnitude of the radiation emitted by a blackbody at an absolute temperature at a…
Step by step
Solved in 3 steps with 1 images
- This a question on Cosmology: Suppose that you have a flat universe that has matter and dark energy with wd = -2/3 & Ωd,0 =0.7 At the time when light with z = 1 was emitted from a distant galaxy what was the ratio Ɛd /Ɛm ?My question is that I don’t understand what happened in the second page from where it says we obtain: I get how we got X but I don’t get how we get alpha in the first page and then use it in the second page till we get the final formula if you can please show me the steps of finding the final formulaIn spherical coordinates, the ladder operators for orbital angular momentum are of the form: eig +icot θ = e-io +i cot 0- Show, by explicit calculation of the relevant products, that these operators satisfy the commutation relations 1. [L,, L4] = ±L+ 2. [L?, L4] = 0. 3. [L4, L-] = 2L.
- Calculation of the gravitational force.1. What is the gravitational force (in N) on a proton at the surface of the Sun?2. At a point mid way to the surface? The average density ρ of the Universe today is 3 × 10−27kgm−3 Find this density in (a) gcm^−3(b) M⊙Mpc^−3(c) mpcm^−32. Find the mass within a sphere of radius (a) R⊙ (b) 1 AU (c) 10 MpWith the aid of a diagram, explain the physical origin of cosmological redshift in an expanding universe, and how this differs from the Doppler shift due to relative motion. Observations of distantgalaxies indicate that their recession velocities, v, and their distances, d, follow a Hubble Law:v = H0d, where H0 is a constant. Using the analogy of an expanding grid or ruler, demonstratethat Hubble’s Law indicates that the Universe is undergoing uniform expansion.Please answer within 90 minutes.
- P2 X The image to the left is a Feynman diagram with time increasing upward. P1 (a) If p1 is an electron and X is a W+ what must p2 be? Why? (b) If p1 is a μ+ and p2 is a different flavor of lepton, what must p2 be? Why? (c) In the last question, what must X be? Why? (d) If p1 and p2 are both electron neutrinos, what must X be? Why? (e) If p1 and p2 are both the same flavor of charged lepton, what might X be? (There are two possibilities.) Why?Suppose that the universe were full of spherical objects, each of mass m and radius r, with the objects distributed uniformly throughout the universe as in the previous problem. (Assume nonrelativistic objects.) Given the density of these spherical objects (as you would have found in the previous problem), how far would you be able to see in meters, on average, before your line of sight intersected one of them? Values (note, different from the above problem): m = 3 kg r = 0.03 m Answer must be in scientific notation and include zero decimal places (1 sig fig).Solve a
- There are two parts to this question. I need to know the years for both. I have tried 14,000,000,000, 17,908,900,000, 17.29 x 10^9, and 17.9089 x 10^9 for the hubble time and all those are wrong. I have tried 17,908,900,000, 17.29 x 10^9, and 17.9089 x 10^9 for the second question and those are wrong too.Briefly explain what is meant by “particle horizon” and “event horizon” in cosmology. Calculate the physical particle horizon, RH(t), at time t. Assume a flat FRW universe whichis dominated by a fluid that gives rise to scale factor evolution where n is a constant with 0 < n < 1, and a(t0) = a0.Subject: physics