That's known as "D20 Queen's Gambit Accepted, 3.e4"
The Queen's Gambit has two points:
- Develop the King's Bishop with tempo
- Take the center that black abandons
in that regard,
3. e4 is the better move though masters play
3. e3 with nearly the same frequency.
I wouldn't worry about the loss of the
c pawn; the purpose of a gambit is to gain time. If you're going to offer a gambit, you must know enough to keep the pressure on, to keep the initiative on your side. If White plays a non-threatening move and Black plays a move with good purpose, White has lost the pawn as well as the time gained when Black took it.
3... b5 is not played often - it's not much of a move. I checked your entire variation; it was only occurred in my masters database 3 times, yielding White 2.5 points.
Here's a master game demonstrating the Queens Gambit Accepted (D20). White has an excellent game up through the middle game seemingly having the game in hand... and then he allows Black to make a passed pawn, and the walls came down.
Robert Aghasaryan vs. Tigran Kotanjian, 1/13/2013
1. d4 d5 2. c4 dxc4 3. Nf3 Nf6 4. e3 e6 5. Bxc4 c5 6. O-O a6 7. dxc5 Qxd1 8. Rxd1 Bxc5 9. Nbd2 b6 10. Be2 Bb7 11. Nc4 Nbd7 12. a3 O-O 13. b4 Be7 14. Bb2 Bd5 15. Nfe5 Nxe5 16. Bxe5 Bxc4 17. Bxc4 a5 18. b5 Rac8 19. Be2 Nd5 20. Bf3 Nc3 21. Rd7 Bf6 22. Bxf6 gxf6 23. Rd6 Rb8 24. a4 Rfc8 25. Rd4 f5 26. Kf1 e5 27. Rd7 Rc4 28. Rc1 Rc5 29. Bh5 Nxa4 30. Bxf7+ Kh8 31. Rxc5 Nxc5 32. Re7 Rb7 33. Re8+ Kg7 34. Bd5 Rd7 35. Rxe5 Kf6 36. f4 a4 37. Ke2 a3 38. Bc4 Ra7 39. Ba2 Ra5 40. Kd2 Rxb5 41. Kc3 Ne4+ 42. Kd4 Rb4+ 43. Kd3 Rb2 44. Re6+ Kg7 0-1
Here's a game where black played
b5. Ruslan Ponomariov vs. Ivan Sokolov, 3/17/2007
1. d4 d5
2. c4 dxc4
3. e4 b5
4. a4 c6
5. axb5 cxb5
6. Nc3 Bd7
7. Nf3 e6
8. Be2 Nf6
9. O-O Be7
10. d5 exd5
11. exd5 Qb6
12. Bf4 Bc5
13. Bxc4 bxc4
14. Qe2+ Kf8
15. Ne5 Bf5
16. Na4 Qb5
17. Nxc5 Qxc5
18. Nxc4 Qd4
19. Be5 Bd3
20. Qd2 Qxd5
21. Rfd1 Qxc4
22. Rac1 Qa6
23. Bxf6 Nd7 (23... gxf6?! 24.Qh6+ Ke7 25.Qe3+ Qe6 26.Qxd3 Nd7 27.Qa3+ Ke8 28.Qa4 Kf8 29.Rxd7 Kg7 30.h3 Rhd8 31.Rxd8 Rxd8 32.Qxa7 Qe2 33.Qb6 Rd2 34.b4 h5 35.Qc5 Rb2 36.Qd4 Qe5 37.Qc4 Qb8 38.Qh4 Qxb4 39.Qxh5)
24. Bc3 Bb5
25. Qg5 Nf6
26. Qc5+ Kg8
27. Bxf6 h6
28. Bc3 Re8
29. Rd6 Qb7
30. Qf5 Qe7
31. Qxb5 1-0
After Black's 6th move, it looks like maybe he'll be able to shove those pawns forward, overpower White's Queen's Knight pawn, and win. Sometimes, advanced pawns are not easy to support. By the end of move 11, both players have developed some pieces but neither side is pushing very hard. Black's Queen on
b6 eyes the perpetually weak
f2 square and the King hiding beyond while threatening, perhaps,
b4. White's 14th exploits Black's uncastled King. Black's response seals in the Rook.
After 17, both Black rooks and a knight are in the box. His King is exposed. He has a good bishop and Knight and his Queen is well placed. His
c pawn looks lonely and has to be defended by the Queen. White has a great Knight and a good Bishop. His isolated
b pawn is sad but not endangered. His
d pawn is kinda hanging out. One of his Rooks is sort of developed and the other has good squares. But White has sacrificed a piece and needs to make something happen.
After move 24, White maintains a slight lead, even though he's down a piece. Black needs to activate his rooks to win. White must not allow this. This is where every tempo counts. White's 25th hits the weak
g7 pawn while his 26th exploits Black's exposed King. White's follow-up,
27. Bxf6 exploits the overloaded Black Queen. It protects the Bishop as well as the Knight since the last thing Black needs is for his pawns to be ripped open with Rooks on the board. if
27... gxf6 then
28. Rc3 followed by
Rg3+ and it's lights-out for Black. White saves his Bishop but the cost is that Black now has time to develop a Rook to
e8. The end of the game isn't spectacular, it looks like Black blundered in time pressure.